Related papers: Soliton solutions for Q3
Focusing on multi-solitons for the Klein-Gordon equations, in first part of this paper, we establish their conditional asymptotic stability. In the second part of this paper, we classify pure multi-solitons which are solutions converging to…
Our purpose of this paper is to study isolated singular solutions of semilinear Helmholtz equation $$ -\Delta u-u=Q|u|^{p-1}u \quad{\rm in}\ \ \mathbb{R}^N\setminus\{0\},\ \qquad\lim_{|x|\to0}u(x)=+\infty, $$ where $N\geq 2$, $p>1$ and the…
We consider 2+1-dimensional classical noncommutative scalar field theory. The general ansatz for a radially symmetric solution is obtained. Some exact solutions are presented. Their possible physical meaning is discussed. The case of the…
Some aspects of the relation between differential geometry of curves and surfaces and multidimensional soliton equations is discussed. The connection between multidimensional soliton equations and Self-dual Yang-Mills equation is studied.
We are interested in the nonlinear damped Klein-Gordon equation \[ \partial_t^2 u+2\alpha \partial_t u-\Delta u+u-|u|^{p-1}u=0 \] on $\mathbb{R}^d$ for $2\le d\le 5$ and energy sub-critical exponents $2 < p < \frac{d+2}{d-2}$. We construct…
We study the $(3+1)$-dimensional eight-order nonlinear wave equation associated with the principal representation of the exceptional affine Lie algebra $E_6^{(1)}$, which was constructed by Kac and Wakimoto and stated that $N$-soliton…
In this article, we investigate the existence and multiplicity of solutions of Kirchhoff equation \begin{equation*} \left\{ \begin{aligned} -(1+b \int_{\mathbb{R}^3}|\nabla u|^2)\Delta u= k(x)\frac{|u|^2 u}{|x|} +\lambda…
In this paper, we establish the soliton resolution for the energy critical wave equation with inverse square potential in the radial case and in all dimensions $N\geq3$. The structure of the radial linear operator $\mathcal{L}_a :=-\Delta…
We present new, unified proofs for the cell-like, $\mathbb{Z}/p$-, and $\mathbb{Q}$-resolution theorems. Our arguments employ extensions that are much simpler then those used by our predecessors. The techniques allow us to solve problems…
We describe an approach to construct multi-soliton asymptotic solutions for non-integrable equations. The general idea is realized in the case of three waves and for the KdV-type equation with nonlinearity $u^4$. A brief review of…
We study a general class of line-soliton solutions of the Kadomtsev-Petviashvili II (KPII) equation by investigating the Wronskian form of its tau-function. We show that, in addition to previously known line-soliton solutions, this class…
We consider the Hirota equation (the discrete analog of the generalized Toda system) over a finite field. We present the general algebro-geometric method of construction of solutions of the equation. As an example we construct analogs of…
We study MNLS related to the D.III-type symmetric spaces. Applying to them Mikhailov reduction groups of the type $\mathbb{Z}_r\times \mathbb{Z}_2$ we derive new types of 2-component NLS equations. These are {\bf not} counterexamples to the…
This paper deals with the cubic-quintic nonlinear Schr\"{o}dinger equation on R^3. Two monotonicity conjectures for solitons posed by Killip, Oh, Pocovnicu and Visan are completely resolved: one concerning frequency monotonicity, and the…
N-fold supersymmetry is an extension of the ordinary supersymmetry in one-dimensional quantum mechanics. One of its major property is quasi-solvability, which means that energy eigenvalues can be obtained for a portion of the spectra. We…
We present an elementary derivation of the soliton-like solutions in the $A_n^{(1)}$ Toda models which is alternative to the previously used Hirota method. The solutions of the underlying linear problem corresponding to the N-solitons are…
We study Baxter's T-Q equation of XXX spin-chain models under the semiclassical limit where an intriguing SU(N)/SU(2)^{N-3} correspondence emerges. That is, two kinds of 4D \mathcal{N}=2 superconformal field theories having the above…
We present a simple approach for finding $N$-soliton solution and the corresponding Jost solutions of the derivative nonlinear Scr\"{o}dinger equation with nonvanishing boundary conditions. Soliton perturbation theory based on the inverse…
We use the generalized Cauchy matrix approach to derive the N-soliton solutions for the (2+2)-dimensional Toda lattice.
Let $\mathbb{F}_q$ be a finite field of $q=p^k$ elements. For any $z\in \mathbb{F}_q$, let $A_n(z)$ and $B_n(z)$ denote the number of solutions of the equations $x_1^3+x_2^3+\cdots+x_n^3=z$ and $x_1^3+x_2^3+\cdots+x_n^3+zx_{n+1}^3=0$…