相关论文: Bell Polynomial Approach and Wronskian Technique t…

Recently, Lembert, Gilson et al proposed a lucid and systematic approach to obtain bilinear B\"{a}cklund transformations and Lax pairs for constant-coefficient soliton equations based on the use of binary Bell polynomials. In this paper, we…

Hirota's bilinear approach is a very effective method to construct solutions for soliton systems. In terms of this method, the nonlinear equations can be transformed into linear equations, and can be solved by using perturbation method. In…

In this paper, we apply the binary Bell polynomial approach to a (2+1) dimensional nonlinear evolution equation. Namely, this study is an integrability work. Bilinear formalism, bilinear Backlund transformation, Lax pair of referred…

In this work, we apply the binary Bell polynomial approach to coupled Burgers system. In other words, we investigate possible integrability of referred system. Bilinear form and soliton solutions are obtained, some figures related to these…

In this paper, we introduce a class of new generalized super Bell polynomials on a superspace, explore their properties, and show that they are a natural and effective tool to systematically investigate integrability of supersymmetric…

An extension of the Laplace transform obtained by using the Laguerre-type exponentials is first shown. Furthermore, the solution of the Blissard problem by means of the Bell polynomials, gives the possibility to associate to any numerical…

The B\"acklund transformation (BT) for the "good" Boussinesq equation and its superposition principles are presented and applied. Unlike many other standard integrable equations, the Boussinesq equation does not have a strictly algebraic…

Polynomials in differentiation operators are considered. The Darboux transformations covariance determines non-Abelian entries to form the coefficients of the polynomials. Joint covariance of a pair of such polynomials (Lax pair) as a…

Partial ordinary Bell polynomials are used to formulate and prove a version of the Fa\`{a} di Bruno's formula which is convenient for handling nonlinear terms in the differential transformation. Applicability of the result is shown in two…

We study rational solutions of the Boussinesq equation, which is a soliton equation solvable by the inverse scattering method. These rational solutions, which are algebraically decaying and depend on two arbitrary parameters, are expressed…

We are concerned with conservation laws and integral relations associated with rational solutions of the Boussinesq equation, a soliton equation solvable by inverse scattering which was first introduced by Boussinesq in 1871. The rational…

In this paper, our goal is to improve the local well-posedness theory for certain generalized Boussinesq equations by revisiting bilinear estimates related to the Schr\"{o}dinger equation. Moreover, we propose a novel, automated procedure…

We present a combinatorial method of constructing solutions to the normal ordering of boson operators. Generalizations of standard combinatorial notions - the Stirling and Bell numbers, Bell polynomials and Dobinski relations - lead to…

The differential transform method is used to find numerical approximation of solution to a class of certain nonlinear differential algebraic equations. The method is based on Taylor's theorem. Coefficients of the Taylor series are…

A broad set of sufficient conditions consisting of systems of linear partial differential equations is presented which guarantees that the Wronskian determinant solves the Korteweg-de Vries equation in the bilinear form. A systematical…

The lattice Boussinesq equation (BSQ) is a three-component difference-difference equation defined on an elementary square of the 2D lattice, having 3D consistency. We write the equations in the Hirota bilinear form and construct their…

A numerical method is developed leading to algebraic systems based on generalized Lyapunov-Sylvester operators to approximate the solution of two-dimensional Boussinesq equation. It consists of an order reduction method and a finite…

Various new two-component systems related to the lattice Schwarzian Boussinesq equation are constructed in a systematic way from conservation laws. Their multidimensional consistency is demonstrated, Lax pairs, symmetries and conservation…

A bilinear formulation for the supersymmetric two-boson equation is derived. As applications, some solutions are calculated for it. We also construct a bilinear Backlund transformation.

A numerical method is developed leading to Lyapunov operators to approximate the solution of two-dimensional Boussinesq equation. It consists of an order reduction method and a finite difference discretization. It is proved to be uniquely…