相关论文: Interaction solutions for mKP equation with nonloc…

The Nonlinear Schr\"odinger (NLS) equation is widely used in everywhere of natural science. Various nonlinear excitations of the NLS equation have been found by many methods. However, except for the soliton-soliton interactions, it is very…

A nonlocal perfectly matched layer (PML) is formulated for the nonlocal wave equation in the whole real axis and numerical discretization is designed for solving the reduced PML problem on a bounded domain. The nonlocal PML poses challenges…

In this paper, using the standard truncated Painleve analysis, the Schwartzian equation of (2+1)-dimensional generalised variable coefficient shallow water wave (SWW)equation is obtained. With the help of lax pairs, nonlocal symmetries of…

Using the reality condition of the solutions, one constructs the real Pfaffian N-solitons solutions of the Novikov-Veselov (NV) equation using the $\tan$ function and the Schur identity. By the minor-summation formula of the Pfaffian, we…

The complex WKB-Maslov method is used to consider an approach to the semiclassical integrability of the multidimensional Gross-Pitaevskii equation with an external field and nonlocal nonlinearity previously developed by the authors.…

The KP-I equation \[ (u_t-2uu_x+\tfrac{1}{2}(\beta-\tfrac{1}{3})u_{xxx})_x -u_{yy}=0 \] arises as a weakly nonlinear model equation for gravity-capillary waves with strong surface tension (Bond number $\beta>1/3$). This equation admits ---…

We introduce a novel meshless simulation method for the McKean-Vlasov Stochastic Differential Equation (MV-SDE) utilizing deep learning, applicable to both self-interaction and interaction scenarios. Traditionally, numerical methods for…

We consider a class of particular solutions to the (2+1)-dimensional nonlinear partial differential equation (PDE) $u_t +\partial_{x_2}^n u_{x_1} - u_{x_1} u =0$ (here $n$ is any integer) reducing it to the ordinary differential equation…

The (1+1)-dimensional higher-order Broer-Kaup (HBK) system is studied by consistent tanh expansion (CTE) method in this paper.It is proved that the HBK system is CTE solvable. Some exact interaction solutions among different nonlinear…

A class of nonlocal nonlinear wave equation arises from the modeling of a one dimensional motion in a nonlinearly, nonlocally elastic medium. The equation involves a kernel function with nonnegative Fourier transform. We discretize the…

In this paper, we study the novel nonlinear wave structures of a (2+1)-dimensional variable-coefficient Korteweg-de Vries (KdV) system by its analytic solutions. Its $N$-soliton solution are obtained via Hirota's bilinear method, and in…

We give the solution to the complete noncommutative Kadomtsev--Petviashvili (KP) hierarchy. We achieve this via direct linearisation which involves the Gelfand--Levitan--Marchenko (GLM) equation. This is a linear integral equation in which…

The finite element method (FEM) is applied to obtain numerical solutions to a recently derived nonlinear equation for the shallow water wave problem. A weak formulation and the Petrov-Galerkin method are used. It is shown that the FEM gives…

In this paper, we study coupled complex modified Korteweg-de Vries (ccmKdV) equation by combining the Hirota's method and the Kadomtsev-Petviashvili (KP) reduction method. First, we show that the bilinear form of the ccmKdV equation under…

In this paper, we primarily construct Darboux transformation(DT) of the nonlocal coupled modified complex integrable dispersionless (cm-CID) equation, which is first proposed by the connection with a nonlocal coupled modified complex short…

Starting from nonlocal symmetries related to B\"acklund transformation (BT), many interesting results can be obtained. Taking the well known potential KdV (pKdV) equation as an example, a new type of nonlocal symmetry in elegant and compact…

We study the maximum wave amplitude produced by line-soliton interactions of the Kadomtsev-Petviashvili II (KPII) equation, and we discuss a mechanism of generation of large amplitude shallow water waves by multi-soliton interactions of…

We construct non-localized, real global solutions of the Kadomtsev-Petviashvili-I equation which vanish for $x\to-\infty$ and study their large time asymptotic behavior. We prove that such solutions eject (for $t\to\infty$) a train of…

We describe the interaction pattern in the $x$-$y$ plane for a family of soliton solutions of the Kadomtsev-Petviashvili (KP) equation, $(-4u_{t}+u_{xxx}+6uu_x)_{x}+3u_{yy}=0$. Those solutions also satisfy the finite Toda lattice hierarchy.…

We discuss an extension of the modified method of simplest equation for obtaining exact analytical solutions of nonlinear partial differential equations. The extension includes the possibility for use of: (i) more than one simplest…