Multiple-scale derivation of the nonlinear Schrödinger equation for solitons in magnetic thin films (abstract)

1997 ◽  
Vol 81 (8) ◽  
pp. 5080-5080
Author(s):  
S. E. Mock ◽  
M. J. Ablowitz ◽  
C. E. Patton
Keyword(s):  
Thin Films ◽  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Multiple Scale ◽  
Magnetic Thin Films ◽  
Nonlinear Schrodinger Equation ◽  
Nonlinear Schrödinger

Slowly varying solitary waves. II. Nonlinear Schrödinger equation

1979 ◽  
Vol 368 (1734) ◽  
pp. 377-388 ◽  
Keyword(s):  
Exact Solution ◽  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Variable Coefficient ◽  
Schrodinger Equation ◽  
Multiple Scale ◽  
Perturbation Parameter ◽  
Nonlinear Schrodinger Equation ◽  
Nonlinear Schrödinger ◽  
Scale Method

The slowly varying solitary wave is constructed as an asymptotic solution of the variable coefficient nonlinear Schrodinger equation. A multiple scale method is used to determine the amplitude and phases of the wave to the second order in the perturbation parameter. The method is similar to that used in (I) (R. Grimshaw 1979 Proc. R. Soc. Lond . A 368, 359). The results are interpreted by using conservation laws. Outer expansions are introduced to remove non-uniformities in the expansion. Finally, when the coefficients satisfy a certain constraint, an exact solution is constructed.

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