Journal
PHYSICA SCRIPTA
Volume 90, Issue 5, Pages -Publisher
IOP PUBLISHING LTD
DOI: 10.1088/0031-8949/90/5/055204
Keywords
time-dependent mass; Lax pair; inverse scattering transform; Gel'fand-Levitan integral equation; soliton; KdV equation
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We show that a time-dependent disturbance term could be embedded into a Korteweg-de Vries (KdV) equation. This is accomplished through a Lax pair formulation of a linearized scattering problem corresponding to the Schrodinger equation. A new generalized KdV equation is obtained by considering the time-dependent mass function. Choosing initial data for the stationary Schrodinger potential, we solve the direct scattering problem. Then, in the inverse scattering problem, the Gel'fand-Levitan integral equation is solved to derive the solution for our new generalized KdV equation. Finally, an elliptic functional form is chosen for the mass function to obtain an elliptic soliton solution.
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