ALBERT

All Library Books, journals and Electronic Records Telegrafenberg

X
feed icon rss

Your email was sent successfully. Check your inbox.

An error occurred while sending the email. Please try again.

Proceed reservation?

Export
  • 1
    Electronic Resource
    Electronic Resource
    Universal and integrable nonlinear evolution systems of equations in 2+1 dimensions (1997)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 38 (1997), S. 4151-4164 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Integrable systems of nonlinear partial differential equations (PDEs) are obtained from integrable equations in 2+1 dimensions, by means of a reduction method of broad applicability based on Fourier expansion and spatio–temporal rescalings, which is asymptotically exact in the limit of weak nonlinearity. The integrability by the spectral transform is explicitly demonstrated, because the corresponding Lax pairs have been derived, applying the same reduction method to the Lax pair of the initial equation. These systems of nonlinear PDEs are likely to be of applicative relevance and have a "universal" character, inasmuch as they may be derived from a very large class of nonlinear evolution equations with a linear dispersive part. © 1997 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.532088
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 2
    Electronic Resource
    Electronic Resource
    The Kadomtsev–Petviashvili equation as a source of integrable model equations (1996)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 37 (1996), S. 6207-6212 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A new integrable and nonlinear partial differential equation (PDE) in 2+1 dimensions is obtained, by an asymptotically exact reduction method based on Fourier expansion and spatiotemporal rescaling, from the Kadomtsev–Petviashvili equation. The integrability property is explicitly demonstrated, by exhibiting the corresponding Lax pair, that is obtained by applying the reduction technique to the Lax pair of the Kadomtsev–Petviashvili equation. This model equation is likely to be of applicative relevance, because it may be considered a consistent approximation of a large class of nonlinear evolution PDEs. © 1996 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.531773
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 3
    Electronic Resource
    Electronic Resource
    A class of integrable Davey–Stewartson type systems (2001)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 42 (2001), S. 2689-2700 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A new integrable Davey–Stewartson type class of systems of partial differential equations in 2+1 dimensions is derived from a previously known integrable equation by means of an asymptotically exact nonlinear reduction method based on Fourier expansion and spatio–temporal rescaling. The integrability by the inverse scattering method is explicitly demonstrated, because the reduction technique is applied to the Lax pair of the starting equation and the corresponding Lax pair of the class of systems of equations is found. The particular characteristics of the reduction method imply that the new systems are likely to be of applicative relevance. © 2001 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.1370396
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 4
    Electronic Resource
    Electronic Resource
    A new integrable Davey–Stewartson-type equation (1999)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 40 (1999), S. 3971-3977 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A new integrable nonlinear partial differential equation (PDE) in 2+1 dimensions is derived starting from the Konopelchenko–Dubrovsky equation. We use an asymptotically exact reduction method based on Fourier expansion and spatio-temporal rescaling and obtain a new integrable Davey–Stewartson-type equation. In order to demonstrate the integrability of the new equation by the inverse scattering method, we apply the reduction technique to the Lax pair of the Konopelchenko–Dubrovsky equation and find the corresponding Lax pair of the new equation. The new equation reduces to the Davey–Stewartson or the nonlinear Schrodinger equation by appropriate limits. © 1999 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.532937
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 5
    Electronic Resource
    Electronic Resource
    A generalized Hirota equation in 2+1 dimensions (1998)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 39 (1998), S. 6547-6551 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Using an asymptotically exact reduction method based on Fourier expansion and spatiotemporal rescaling, a new integrable and nonlinear partial differential equation (PDE) in 2+1 dimensions is obtained starting from the Kadomtsev–Petviashvili equation. We apply the reduction technique to the Lax pair of the Kadomtsev–Petviashvili equation and demonstrate the integrability property of the new equation, because we obtain the corresponding Lax pair. The new equation reduces to the Hirota equation in the 1+1-dimensional limit. © 1998 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.532664
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 6
    Electronic Resource
    Electronic Resource
    Saddle-Node Bifurcations of Cycles in a Relief Valve (2000)
    Springer
    Nonlinear dynamics 22 (2000), S. 225-247 
    Details
    ISSN: 1573-269X
    Keywords: perturbation methods ; relief valve ; primary resonance ; subharmonic resonance ; combination resonance
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We extend the asymptotic perturbation (AP) method to the studyof a linear partial differential equation with nonlinear boundaryconditions. A relief valve under the combined effects of static anddynamic loadings is considered with the following resonances between thenth linear mode and the external periodic excitation: primaryresonance, subharmonic resonance of order one-half or one-third,superharmonic resonance of order-two or order-three and combinationresonance. The AP method uses two different procedures for thesolutions: introducing an asymptotic temporal rescaling and balancing ofthe harmonic terms with a simple iteration. We obtain amplitude andphase modulation equations and determine external force-response andfrequency-response curves. Stability of steady-state motions is alsoinvestigated. Saddle-node bifurcations of cycles are observed and underappropriate conditions the performance of the relief valve may beunsatisfactory due to the presence of jumps and hysteresis effects inthe system response. Global analysis is used in order to exclude theexistence of modulated motion. The validity of the method is highlightedby comparing approximate solutions with results of the numericalintegration.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1008349500673
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 7
    Electronic Resource
    Electronic Resource
    Approximate Solution of a Class of Nonlinear Oscillators in Resonance with a Periodic Excitation (1998)
    Springer
    Nonlinear dynamics 15 (1998), S. 329-343 
    Details
    ISSN: 1573-269X
    Keywords: Nonlinear oscillation ; limit cycle ; asymptotic analysis
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract This paper deals with the most important characteristics of a generalized Van der Pol–Duffing oscillator in resonance with a periodic excitation. We use an asymptotic perturbation method based on Fourier expansion and time rescaling and demonstrate through a second order perturbation analysis the existence of one or two limit cycles. Moreover, we identify a sufficient condition to obtain a doubly periodic motion, when a second low frequency appears, in addition to the forcing frequency. Comparison with the solution obtained by the numerical integration confirms the validity of our analysis.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1008235820302
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 8
    Electronic Resource
    Electronic Resource
    The Dissipative Nonlocal Oscillator (1998)
    Springer
    Nonlinear dynamics 16 (1998), S. 307-320 
    Details
    ISSN: 1573-269X
    Keywords: Nonlocal oscillator ; bifurcations ; limit cycles ; quasi-periodic motion
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The most important characteristics of a nonlocal and nonlinear oscillator subject to dissipative forces are extensively studied by means of an asymptotic perturbation method, based upon temporal rescaling and harmonic balance. The conditions under which bifurcations and limit cycles appear are determined. If the parameters satisfy particular conditions, a quasi-periodic motion is predicted, because a second small frequency adds to the natural frequency of the oscillator. The analytical results are validated by numerically solving the original system.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1008290009964
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 9
    Electronic Resource
    Electronic Resource
    The Asymptotic Perturbation Method for Nonlinear Continuous Systems (1999)
    Springer
    Nonlinear dynamics 19 (1999), S. 1-18 
    Details
    ISSN: 1573-269X
    Keywords: perturbation methods ; nonlinear foundation ; primary resonance ; subharmonic resonance
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We apply the asymptotic perturbation (AP) method to the study of the vibrations of Euler--Bernoulli beam resting on a nonlinear elastic foundation. An external periodic excitation is in primary resonance or in subharmonic resonance in the order of one-half with an nth mode frequency. The AP method uses two different procedures for the solutions: introducing an asymptotic temporal rescaling and balancing the harmonic terms with a simple iteration. We obtain amplitude and phase modulation equations and determine external force-response and frequency-response curves. The validity of the method is highlighted by comparing the approximate solutions with the results of the numerical integration and multiple-scale methods.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1008304701252
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 10
    Electronic Resource
    Electronic Resource
    A Perturbation Method for Nonlinear Two-Dimensional Maps (1999)
    Springer
    Nonlinear dynamics 19 (1999), S. 295-312 
    Details
    ISSN: 1573-269X
    Keywords: perturbation methods ; bifurcations ; discrete nonlinear maps ; almost-periodic solutions
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A new perturbation method for a weakly nonlinear two-dimensional discrete-time dynamical system is presented. The proposed technique generalizes the asymptotic perturbation method that is valid for continuous-time systems and detects periodic or almost-periodic orbits and their stability. Two equations for the amplitude and the phase of solutions are derived and their fixed points correspond to limit cycles for the starting nonlinear map. The method is applied to various nonlinear (autonomous or not) two-dimensional maps. For the autonomous maps we derive the conditions for the appearance of a supercritical Hopf bifurcation and predict the characteristics of the corresponding limit cycle. For the nonautonomous maps we show amplitude-response and frequency-response curves. Under appropriate conditions, we demonstrate the occurrence of saddle-node bifurcations of cycles and of jumps and hysteresis effects in the system response (cusp catastrophe). Modulated motion can be observed for very low values of the external excitation and an infinite-period bifurcation occurs if the external excitation increases. Analytic approximate solutions are in good agreement with numerically obtained solutions.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1008354207308
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
Close ⊗
This website uses cookies and the analysis tool Matomo. More information can be found here...