Self-similar solutions of certain coupled integrable systems
نویسندگان
چکیده
Similarity reductions of the coupled nonlinear Schrödinger equation and an integrable version of the coupled Maxwell-Bloch system are obtained by applying non-translational symmetries. The reduced system of coupled ordinary differential equations are solved in terms of Painlevé transcendents, leading to new exact self-similar solutions for these integrable equations. PACS numbers: 02.30.Ik., 02.30.Hq., 02.30.Gp.
منابع مشابه
Solution and stability analysis of coupled nonlinear Schrodinger equations
We consider a new type of integrable coupled nonlinear Schrodinger (CNLS)equations proposed by our self [submitted to Phys. Plasmas (2011)]. The explicitform of soliton solutions are derived using the Hirota's bilinear method.We show that the parameters in the CNLS equations only determine the regionsfor the existence of bright and dark soliton solutions. Finally, throughthe linear stability an...
متن کاملSelf-similar solutions of the Riemann problem for two-dimensional systems of conservation laws
In this paper, a new approach is applied to study the self-similar solutions of 2×2 systems of nonlinear hyperbolic conservation laws. A notion of characteristic directions is introduced and then used to construct local and smooth solutions of the associated Riemann problem
متن کاملA modified homotopy perturbation method to periodic solution of a coupled integrable dispersionless equation
In this paper, a reliable approach is introduced to approximate periodic solutions of a system of coupled integrable dispersionless. The system is firstly, transformed into an ordinary differential equation by wave transformation. The solution of ODE is obtained by the homotopy perturbation method. To show the periodic behavior of the solution, a modification based on the Laplace transforms and...
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 کاملNew reductions of integrable matrix PDEs — Sp ( m ) - invariant systems —
We propose a new type of reduction for integrable systems of coupled matrix PDEs; this reduction equates one matrix variable with the transposition of another multiplied by an anti-symmetric constant matrix. Via this reduction, we obtain a new integrable system of coupled derivative mKdV equations and a new integrable variant of the massive Thirring model, in addition to already known systems. ...
متن کامل