ISSN:
1089-7658
Source:
AIP Digital Archive
Topics:
Mathematics
,
Physics
Notes:
In a recent paper, Brüll and Lange [Expos. Math. 4, 279 (1986); Math. Meth. Appl. Sci. 8, 559 (1986)] have discussed a class of nonlinear Schrödinger equations with rather general nonlinearities which comprises various cases occurring in the literature. Although the "potentials'' in these equations are quite complicated, the equations admit various invariance properties. The present paper has two aims. First several local and global conservation laws related to conservation of mass, impulse, and energy are exhibited. One of these laws seems to be new, though not surprising. Then it is shown that the equation defined by Brüll and Lange is just suitable to apply some transformations which reduce the problem of solitary waves to a relatively simple Hamiltonian system in the plane. This method of transforming the phase plane problem into normal form is, in some respects, similar to the transformations introduced by Hadeler [Proc. Math. Soc. Edinburgh, to be published; Free Boundary Problems: Theory and Applications, Montecatini Conference, 1981, edited by A.Fasano and M. Primicerio (Pitman, New York, 1983), Vol. II, pp. 664–671] for parabolic and hyperbolic reaction diffusion equations.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1063/1.527552
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