Thus the complete pattern of the soliton theory is revealed.Pan Zu-Liang and Zheng Ke-Jie and Zhao Shen-QiChaos, Solitons & FractalsPan Zu-liang,Zhao Shen-Qi,Zheng Ke-jie. An algebraic method for solving the KdV equation (Ⅱ). Three-parameter and four-parameter solution family[Z]. Chaos...
In Section 2, the MSFP method for the two-dimensional Hamiltonian PDE (2D-HPDE) is constructed. In Sections 3 The multi-symplectic Fourier pseudospectral method for solving the Zakharov–Kuznetsov equation, 4 The multi-symplectic Fourier pseudospectral method for solving the Kadomtsev–Petviashvili ...
for solving different kinds of physical and mathematical problems. Among those methods are: the homotopy perturbation method [1-7], the variational it- eration method [8-22] and the domain decomposition method [23]. An elementary introduction to the homo- topy perturbation method can be found ...
The method of lines and Adomian decomposition for obtaining solitary wave solutions of the KdV equation, Applied Physics Research, 5 (2013) 43-57.Mousa MM and Reda M (2013). The method of lines and Adomian decomposition for obtaining solitary wave solutions of the KdV equation.Applied Physics ...
Test equation of the type Eq. (1) is also considered in [12, 13]. In these works, the authors applied the separation of the variables to solve analytically. The finite element method (FEM) is a well-established numerical method for solving partial differential equations (PDEs). The method...
A sub-equation method for solving the cubic–quartic NLSE with the Kerr law nonlinearity Hadi Rezazadeh, Ahmad Neirameh, Mostafa Eslami, Ahmet Bekir, and Alper Korkmaz Modern Physics Letters BVol. 33, No. 18 Lump soliton wave solutions for the (2+1)-dimensional Konopelchenko–Dubrovsky equat...
The (G′/G, 1/G)– expansion method for solving Eq. (1) proceeds in the following steps: Step 1: Look for traveling wave solution of Eq. (1) by taking(2)P=P(ξ),ξ=x+y-Vt,where V is nonzero constant, P(ξ) the function of ξ. Substituting (2) into Eq. (1) yields an...
The paper is devoted to the construction of singular solutions of the KdV equation. The presentation is based on a variant of the inverse scattering method for singular solutions of nonlinear equations developed in previous works of the authors....
In this work we use the tanh method for solving several forms of the fifth-order nonlinear KdV equation. The forms include the Lax, Sawada–Kotera (SK), Kaup–Kupershmidt (KK), and the Ito forms and other related special cases. Abundant solitons solutions are derived. Two necessary criteria...
methods called the variational iteration method (VIM) andthe variational homotopy perturbation method (VHPM) are introduced to obtain the exact and thenumerical solutions of the (2+1)-dimensional Korteweg-de Vries-Burgers (KdVB) equation and the(1+1)-dimensional Sharma-Tasso-Olver equation. The...