相关论文: Notes on solutions in Wronskian form to soliton eq…

The Cosserat model generalises an elastic material taking into account the possible microstructure of the elements of the material continuum. In particular, within the Cosserat model the structured material point is rigid and can only…

Early results concerning the linear stability of the solitons in equation of the KDV-type \cite{KUZNETSOV1984314} are generalized to solitons describing by the ZK-type equation. The linear stability criterion for ground solitons in the…

The Korteweg-de Vries equation is a fundamental nonlinear equation that describes solitons with constant velocity. On the contrary, here we show that this equation also presents accelerated wavepacket solutions. This behavior is achieved by…

A Hamiltonian approach to the solution of the Vlasov-Poisson equations has been developed. Based on a nonlinear canonical transformation, the rapidly oscillating terms in the original Hamiltonian are transformed away, yielding a new…

Using new generalized Landen transformations, we prove that the solutions of the KdV and other nonlinear equations obtained recently by using a kind of superposition principle for periodic solutions are in fact novel re-expressions of well…

Elliptic soliton solutions, i.e., a hierarchy of functions based on an elliptic seed solution, are constructed using an elliptic Cauchy kernel, for integrable lattice equations of Kadomtsev-Petviashvili (KP) type. This comprises the lattice…

The purpose of this paper is to make a few connections among specific concepts occurring in differential geometry and the theory of differential equations with the aim of identifying an intriguing class of undetermined nonlinear ordinary…

We consider the WDVV associativity equations in the four dimensional case. These nonlinear equations of third order can be written as a pair of six component commuting two-dimensional non-diagonalizable hydrodynamic type systems. We prove…

This is a brief review of recent progress in constructing solutions to the matrix model Virasoro equations. These equations are parameterized by a degree n polynomial W_n(x), and the general solution is labeled by an arbitrary function 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 consider the Wilson line networks of the Chern-Simons $3d$ gravity theory with toroidal boundary conditions which calculate global conformal blocks of degenerate quasi-primary operators in torus $2d$ CFT. After general discussion that…

We propose a numerical method for finding solitary wave solutions of generalized Korteweg-de Vries equations by solving the nonlinear eigenvalue problem on an unbounded domain. The artificial boundary conditions are obtained to make the…

Some of the well-known convergence acceleration algorithms, when viewed as two-variable difference equations, are equivalent to discrete soliton equations. It is shown that the $\eta-$algorithm is nothing but the discrete KdV equation. In…

We give a simple geometric interpretation of the mapping of the negative KdV equation as proposed by Qiao and Li {arXiv:1101.1605 [math-ph], Europhys. Lett.,94 (2011) 50003} and the Fuchssteiner equation using geometry of projective…

We consider the regularity of stationary solutions to the linearized Boltzmann equations in bounded $C^1$ convex domains in $\mathbb{R}^3$ for gases with cutoff hard potential and cutoff Maxwellian gases. We prove that the stationary…

We first study coupled Hirota-Iwao modified KdV (HI-mKdV) systems and give all possible local and nonlocal reductions of these systems. We then present Hirota bilinear forms of these systems and give one-soliton solutions of them with the…

The purpose of this paper is to bridge the gap between the Dbar method and the direct linearization approach for the lattice Korteweg-de Vries (KdV) type equations. We develop the Dbar method to study some discrete integrable equations in…

We find explicit (multisoliton) solutions for nonabelian integrable systems such as periodic Toda field equations, Langmuir equations, and Schrodinger equations for functions with values in any associative algebra. The solution for…

A procedure to construct $K$-matrices from the generalized $q$-Onsager algebra $\cO_{q}(\hat{g})$ is proposed. This procedure extends the intertwiner techniques used to obtain scalar (c-number) solutions of the reflection equation to…

We study soliton solutions to the DKP equation which is defined by the Hirota bilinear form, \[ {\begin{array}{llll} (-4D_xD_t+D_x^4+3D_y^2) \tau_n\cdot\tau_n=24\tau_{n-1}\tau_{n+1}, (2D_t+D_x^3\mp 3D_xD_y) \tau_{n\pm 1}\cdot\tau_n=0…