In this paper, we derive a new method for a nonlinear Schrodinger system by using the square of the first-order Fourier spectral differentiation matrix D1 instead of the traditional second-order Fourier spectral differentiation matrix D2 to approximate the second derivative. We prove that the proposed method preserves the charge and energy conservation laws exactly. A deduction argument is used to prove that the numerical solution is second-order convergent to the exact solutions in ｜｜·｜｜2 norm. Some numerical results are reported to illustrate the efficiency of the new scheme in preserving the charge and energy conservation laws.
We propose multisymplectic implicit and explicit Fourier pseudospectral methods for the Klein-Gordon-Schrodinger equations.We prove that the implicit method satisfies the charge conservation law exactly.Both methods provide accurate solutions in long-time computations and simulate the soliton collision well.The numerical results show the abilities of the two methods in preserving the charge,energy,and momentum conservation laws.
In this paper,we derive a multi-symplectic Fourier pseudospectral scheme for the Kawahara equation with special attention to the relationship between the spectral differentiation matrix and discrete Fourier transform.The relationship is crucial for implementing the scheme efficiently.By using the relationship,we can apply the Fast Fourier transform to solve the Kawahara equation.The effectiveness of the proposed methods will be demonstrated by a number of numerical examples.The numerical results also confirm that the global energy and momentum are well preserved.
