The inverse scattering transformation for a novel nonlocal Lakshmanan–Porsezian–Daniel (LPD) equation with rapidly decaying initial data is studied in the framework of Riemann–Hilbert problem. Firstly, integrable LPD corresponding to $$3\times 3$$ Lax pair proposed. Secondly, process left-right matrix Riemann–Hilbert(RH) problem constructed. analytical properties and symmetry relations Jost fun...

A theory for constructing integrable couplings of soliton equations is developed by using various perturbations around solutions of perturbed soliton equations being analytic with respect to a small perturbation parameter. Multi-scale perturbations can be taken and thus higher dimensional integrable couplings can be presented. The theory is applied to the KdV soliton hierarchy. Infinitely many ...

In the process of searching for explicit solutions, quite a few systematic methods have been developed, such as inverse scattering transformation [1], Darboux transformations [2], Hirota’s bilinear method [3-5], and so on. Among them, the bilinear method first proposed by Hirota provides us with a comprehensive approach to construct exact solutions of nonlinear evolution equations (NEEs). Meanw...

In this paper, a generalized simplest equation method is proposed to seek exact solutions of nonlinear evolution equations (NLEEs). In the method, we chose a solution expression with a variable coefficient and a variable coefficient ordinary differential auxiliary equation. This method can yield a Bäcklund transformation between NLEEs and a related constraint equation. By dealing with the const...

a modified f-expansion method to find the exact traveling wave solutions of  two-component nonlinear partial differential equations (nlpdes) is discussed. we use this method to construct many new solutions to the nonlinear whitham-broer-kaup system (1+1)-dimensional. the solutions obtained include jacobi elliptic periodic wave solutions which exactly degenerate to the soliton solutions, triangu...

In this present study analytical method based on Riccati Equation as for converting the Nonlinear Lakshmanan-Porsezian-Daniel (LPD) equation into the nonlinear ODE and finding soliton solutions of this sustem discused. Obtaining solutions are new and obtained from wave transformation. The obtained results show that the presented method is effective and appropriate for solving nonlinear differen...

We consider N-soliton solutions of the KP equation, (−4ut + uxxx + 6uux)x + 3uyy = 0 . An N-soliton solution is a solution u(x, y, t) which has the same set of N line soliton solutions in both asymptotics y → ∞ and y → −∞. The N-soliton solutions include all possible resonant interactions among those line solitons. We then classify those N-soliton solutions by defining a pair of N-numbers (n,n)...

A bstract We study dynamics of multi-soliton solutions anti-self-dual Yang-Mills equations for G = GL(2 , ℂ) in four-dimensional spaces. The one-soliton solution can be interpreted as a codimension-one soliton spaces because the principal peak action density localizes on three-dimensional hyperplane. call it wall. prove that asymptotic region, n -soliton possesses isolated localized lumps densi...