Soliton solutions of non-linear Schrodinger (NLS) and Korteweg de Vries (KdV) equations related to zero curvature in the x,t plane

Details Soliton solutions of non-linear Schrodinger (NLS) and Korteweg de Vries (KdV) equations related to zero curvature in the x,t plane Soliton solutions of non-linear Schrodinger (NLS) and Korteweg de Vries (KdV) equations related to zero curvature in the x,t plane

2011-11-21

arxiv.org/abs/1111.5226v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

15 pages

Scientific paper

Soliton solutions of non-linear NLS and KdV equations are related to compatibility condition between matrices M and H describing the movement of an auxilary function Psi in the x,t plane with a zero curvature condition. Non-linear equation for a function u is obtained by the compatibility equation where the matrix elements of M and H include only functions of u and its derivatives. By solving the equations of motion for Psi a soliton solution for u is obtained. Explicit calculations are made with two-dimensional and one-dimensional wave functions Psi for the NLS and KdV solitons, correspondingly.

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