and Casorati Determinant Solutions to Non - autonomous 1 + 1 Dimensional Discrete Soliton Equations ( Expansion of Integrable Systems
نویسندگان
چکیده
Some techniques of bilinearization of the non-autonomous 1+1 dimensional discrete soliton equations are discussed by taking the discrete KdV equation, the discrete Toda lattice equation, and the discrete Lotka-Volterra equation as examples. Casorati determinant solutions to those equations are also constructed explicitly. §
منابع مشابه
Bilinearization and Casorati determinant solutions to non-autonomous 1+1 dimensional discrete soliton equations
Some techniques of bilinearization of the non-autonomous 1 + 1 dimensional discrete soliton equations is discussed by taking the discrete KdV equation, the discrete Toda lattice equation, and the discrete LotkaVolterra equation as examples. Casorati determinant solutions to those equations are also constructed explicitly.
متن کاملDeterminant Form of Dark Soliton Solutions of the Discrete Nonlinear Schrödinger Equation
It is shown that the N-dark soliton solutions of the integrable discrete nonlinear Schrödinger (IDNLS) equation are given in terms of the Casorati determinant. The conditions for reduction, complex conjugacy and regularity for the Casorati determinant solution are also given explicitly. The relationship between the IDNLS and the relativistic Toda lattice is discussed.
متن کاملCasorati Determinant Form of Dark Soliton Solutions of the Discrete Nonlinear Schrödinger Equation
is one of most important soliton equations in mathematics and physics. The study of discrete analogues of the NLS equation has received considerable attention recently from both physical and mathematical point of view.1, 2 The integrable discrete nonlinear Schrödinger (IDNLS) equation is given by i dψn dt = ψn+1 + ψn−1 + α|ψn|(ψn+1 + ψn−1) . (1.2) The IDNLS equation was originally derived by Ab...
متن کاملIntegrable discretizations and self-adaptive moving mesh method for a coupled short pulse equation
In the present paper, integrable semi-discrete and fully discrete analogues of a coupled short pulse (CSP) equation are constructed. The key to the construction are the bilinear forms and determinant structure of the solutions of the CSP equation. We also construct N-soliton solutions for the semi-discrete and fully discrete analogues of the CSP equations in the form of Casorati determinants. I...
متن کاملNew explicit and Soliton Wave Solutions of Some Nonlinear Partial Differential Equations with Infinite Series Method
To start with, having employed transformation wave, some nonlinear partial differential equations have been converted into an ODE. Then, using the infinite series method for equations with similar linear part, the researchers have earned the exact soliton solutions of the selected equations. It is required to state that the infinite series method is a well-organized method for obtaining exact s...
متن کامل