可精确求解与可积系统

In this paper, we aim to investigate the mixed Chen-Lee-Liu derivative nonlinear Schr\"{o}dinger(CLL-NLS) equation via the Riemann-Hilbert(RH) method. we construct a RH problem base on the Jost solution of the Lax pair. By solving this RH…

We study higher order KdV equations from the GL(2,$\mathbb{R}$) $\cong$ SO(2,1) Lie group point of view. We find elliptic solutions of higher order KdV equations up to the ninth order. We argue that the main structure of the…

We study a discrete Darboux transformation and construct the multi-soliton solutions in terms of ratio of determinants for integrable discrete sine-Gordon equation. We also calculate explicit expressions of single, double, triple, quad…

Novel soliton structures are constructed for the Fokas-Lenells equation. In so doing, and after discussing the stability of continuous waves, a multiple scales perturbation theory is used to reduce the equation to a Korteweg-de Vries system…

We construct a three-component system of PDEs describing dynamics of van der Walls gas in one-dimensional nozzle. The group of conservation laws for this system is described. We also ompute the Lie algebras of point symmetries and present…

We study to unify soliton systems, KdV/mKdV/sinh-Gordon, through SO(2,1) $\cong$ GL(2,$\mathbb R$) $\cong$ M\"{o}bius group point of view, which might be a keystone to exactly solve some special non-linear differential equations. If we…

For generalized 2D Ising model in an external magnetic field with the interaction of nearest neighbors, next nearest neighbors, all kinds of triple interactions and the quadruple interaction the formulas for finding free energy per lattice…

In this paper, an extended nonlinear Schrodinger equation with higher-order that includes fifth-order dispersion with matching higher-order nonlinear terms is investigated under zero boundary condition at infinity. Carrying out the spectral…

An arbitrary compact-support initial datum for the Korteweg-de Vries equation asymptotically splits into solitons and a radiation tail, moving in opposite direction. We give asimple method to predict the number and amplitudes of resulting…

We present a recursion operator and an infinite hierarchy of nonlocal commuting symmetries for the modified Martinez Alonso-Shabat equation $u_y u_{xz} + \alpha u_x u_{ty} - (u_z + \alpha u_t)u_{xy} = 0$.

We derive new Lax representations for the hyper-CR equation of Einstein--Weyl structures and for the associated integrable hierarchy.

Due to the widely applications in almost all branches of science, high dimensional KP equation is selected as universal model to describe rogue wave phenomenon. A lump is an algebraically localized wave decayed in all space directions and…

We construct the hierarchy of a multi-component generalisation of modified KdV equation and find exact solutions to its associated members. The construction of the hierarchy and its conservation laws is based on the Drinfel'd-Sokolov…

We study the fundamental rogue wave solutions of the focusing nonlinear Schr\"odinger equation in the limit of large order. Using a recently-proposed Riemann-Hilbert representation of the rogue wave solution of arbitrary order $k$, we…

We proposed general scheme for construction of exact real periodical solutions of mKP-1 equation via Zakharov-Manakov $\overline{\partial}$-dressing method, derived convenient determinant formula for calculation of such solutions and…

We constructed new classes of exact multi-lump solutions of mKP-1,2 equations with integrable boundary condition $u(x,y,t)\big|_{y=0}=0$ by the use of $\overline\partial$-dressing method of Zakharov and Manakov. We exactly satisfied reality…

In this article, we study the generalised Kudryashov method for the time fractional generalized Burgers-Fisher equation (GBF). Using traveling wave transformation, the time fractional GBF is transformed to nonlinear ordinary differential…

In this article, we study the Lie point symmetries for the time fractional generalized Burgers-Fisher (GBF) equation. While getting an appropriate combination of symmetries, the time fractional partial differential equation has been…

The focusing Nonlinear Schr\"odinger (NLS) equation is the simplest universal model describing the modulation instability (MI) of quasi monochromatic waves in weakly nonlinear media, and MI is considered the main physical mechanism for the…

In this article, we give the trigonal Toda lattice equation, $$ -\frac{1}{2}\frac{d^3}{d t^3} q_{\ell}(t) = e^{q_{\ell+1}(t)} +e^{q_{\ell+\zeta_3}(t)} +e^{q_{\ell+\zeta_3^2}(t)}-3e^{q_\ell(t)}, $$ for a lattice point $\ell \in…