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Numerical study of the soliton waves of the coupled nonlinear Schrödinger system. (English) Zbl 1056.65083
Summary: A new six-point scheme of the coupled nonlinear Schrödinger (CNLS) system is derived from the symplectic scheme to study the collision behaviors of soliton waves. We prove that the new six-point scheme preserves the square conservation, which matches the square conservation of the CNLS system. Numerical experiments show that the new six-point scheme has excellent long-time numerical behaviors. From the numerical experiment results we find that the collisions of the soliton waves in the CNLS system are sensitive to the collision velocity and the cross-phase-modulational coefficient.

MSC:
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
35Q55 NLS equations (nonlinear Schrödinger equations)
35Q51 Soliton equations
37M15 Discretization methods and integrators (symplectic, variational, geometric, etc.) for dynamical systems
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