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Digitale Medien

An effective method to compute N-fold Darboux matrix and N-soliton surfaces (1991)

Cies´linski, Jan

College Park, Md. : American Institute of Physics (AIP)

Journal of Mathematical Physics 32 (1991), S. 2395-2399

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ISSN: 1089-7658

Quelle: AIP Digital Archive

Thema: Mathematik , Physik

Notizen: Fairly simple formulas for an N-fold Darboux matrix and an N-soliton addition to an arbitrary soliton surface embedded in E3 are proven. They depend directly on the background wave function and are evidently symmetric with respect to N added solitons. As an example, an explicit expression for the interaction of N solitons on a single vortex filament is presented. Moreover, there is given a simplified version of the N-soliton formulas of Neugebauer and Meinel.

Materialart: Digitale Medien

URL: http://dx.doi.org/10.1063/1.529165

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Digitale Medien

Group interpretation of the spectral parameter in the case of nonhomogeneous, nonlinear Schrödinger system (1993)

Cies´linski, Jan

College Park, Md. : American Institute of Physics (AIP)

Journal of Mathematical Physics 34 (1993), S. 2372-2384

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ISSN: 1089-7658

Quelle: AIP Digital Archive

Thema: Mathematik , Physik

Notizen: A one-parameter group inserting the spectral parameter into the nonparametric Lax pair of the nonhomogeneous, nonlinear Schrödinger system is presented and discussed. Being a nonlocal extension of a Lie point transformation this group is probably not contained in any known class of symmetries.

Materialart: Digitale Medien

URL: http://dx.doi.org/10.1063/1.530122

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3

Digitale Medien

An algebraic method to construct the Darboux matrix (1995)

Cies´linski, Jan

College Park, Md. : American Institute of Physics (AIP)

Journal of Mathematical Physics 36 (1995), S. 5670-5706

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ISSN: 1089-7658

Quelle: AIP Digital Archive

Thema: Mathematik , Physik

Notizen: We present an effective procedure to construct the 1-soliton Darboux matrix. Our approach, based on the Zakharov–Shabat–Mikhailov's dressing method, is especially useful in the case of non-canonical normalization and for non-isospectral linear problems. The construction is divided into two steps. First, we represent a given linear problem as a system of some algebraic constraints on two matrices. In this context we introduce and discuss invariants of the Darboux matrix. Second, we derive the Darboux matrix demanding that it preserves the algebraic constraints. In particular, we consider in details the restrictions imposed by various reduction groups on the form of the Darboux matrix. © 1995 American Institute of Physics.

Materialart: Digitale Medien

URL: http://dx.doi.org/10.1063/1.531282

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Digitale Medien

A generalized formula for integrable classes of surfaces in Lie algebras (1997)

Cies´linski, Jan

College Park, Md. : American Institute of Physics (AIP)

Journal of Mathematical Physics 38 (1997), S. 4255-4272

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ISSN: 1089-7658

Quelle: AIP Digital Archive

Thema: Mathematik , Physik

Notizen: We discuss relations between the approach of Fokas and Gelfand to immersions on Lie algebras and the theory of soliton surfaces of Sym. We show that many results concerning immersions on Lie algebras can be reduced to or interpreted within the soliton surfaces approach. We present also some new results, including a generalization of the Fokas–Gelfand formula for integrable classes of surfaces in Lie algebras [and, in particular, in (pseudo)-Euclidean n-dim. spaces]. The generalized formula is used to formulate a method of constructing integrable classes of surfaces. As an example we discuss the class of linear Weingarten surfaces defined by the linear relationship between Gaussian and mean curvatures. We construct explicitly a one-parameter family of linear Weingarten surfaces parallel (equidistant) to a given pseudospherical surface. © 1997 American Institute of Physics.

Materialart: Digitale Medien

URL: http://dx.doi.org/10.1063/1.532093

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