Related papers: Two-component nonlinear wave of the Hirota equatio…
We derive a novel two-component generalization of the nonlinear variational wave equation as a model for the director field of a nematic liquid crystal with a variable order parameter. The two-component nonlinear variational wave equation…
In this paper we derive a two-component system of nonlinear equations which model two-dimensional shallow water waves with constant vorticity. Then we prove well-posedness of this equation using a geometrical framework which allows us to…
This is a continuation of Ref.[1](arXiv:nlin.PS/2001.07758v1). In the present paper, we consider the solution to the modified Benjamin-Bona-Mahony equation $u_{ t} + C u_{z} + \beta u_{zzt} + a u^{2} u_{z}=0$ using the generalized…
Physically relevant soliton solutions of the resonant nonlinear Schrodinger (RNLS) equation with nontrivial boundary conditions, recently proposed for description of uniaxial waves in a cold collisionless plasma, are considered in the…
The Schr\"odinger-like equations for the marginal and conditional probability amplitudes resulting from the exact factorization of the wavefunction of a two-component system are derived in a form that is invariant to gauge and coordinate…
Considering the coupled envelope equations in nonlinear couplers, the question of integrability is attempted. It is explicitly shown that Hirota's bilinear method is one of the simple and alternative techniques to Painlev\'e analysis to…
Based on a Riemann theta function and Hirota's bilinear form, a lucid and straightforward way is presented to explicitly construct double periodic wave solutions for both nonlinear differential and difference equations. Once such a equation…
In this paper, based on the nonlinear fractional equations proposed by Ablowitz, Been, and Carr in the sense of Riesz fractional derivative, we explore the fractional coupled Hirota equation and give its explicit form. Unlike the previous…
The nonlinear coherent interaction of light with the dispersive and Kerr-type third-order susceptibility medium containing optical impurity atoms or semiconductor quantum dots is considered. Using the generalized perturbation reduction…
Using the very basic physics principles, we have studied the implications of quantum corrections to classical electrodynamics and the propagation of electromagnetic waves and pulses. The initial nonlinear wave equation for the…
In a previous work[1] exact stable oblique soliton solutions were revealed in two dimensional nonlinear Schroedinger flow. In this work we show that single soliton solution can be expressed within the Hirota bilinear formalism. An attempt…
A condition of reduction of multidimensional wave equations to the two-dimensional equation is studied, and the necessary conditions of compatibility and exact solutions of the resulting d'Alembert-Hamilton system are obtained.
In the present paper, we mainly study the integrable semi-discretization of a multi-component short pulse equation. Firstly, we briefly review the bilinear equations for a multi-component short pulse equation proposed by Matsuno (J. Math.…
In this paper, We extend the two-component coupled Hirota equation to the three-component one, and reconstruct the Lax pair with $4\times4$ matrixes of this three-component coupled system including higher-order effects such as third-order…
Schrodinger equation with two-component wave function which describes a relativistic spin 1/2 particle in a weak electromagnetic field is obtained. In the same approximation Schrodinger equation with traditional norm condition and…
The Hirota equation is an integrable higher order nonlinear Schr\"{o}dinger type equation which describes the propagation of ultrashort light pulses in optical fibers. We present a standard Darboux transformation for the Hirota equation and…
A nonrelativistic equation for the system of two interacting particles within the framework of a model with noncommuting operators of coordinates and momenta of different particles is proposed, and a self-consistent system of equations for…
In this paper, we study the following two-component systems of nonlinear Schr\"odinger equations \begin{equation*} \left\{\aligned&\Delta u-(\lambda a(x)+a_0(x))u+\mu_1u^3+\beta v^2u=0\quad&\text{in }\bbr^3,\\ &\Delta v-(\lambda…
The higher-order dispersive and nonlinear effects (alias {\it the perturbation terms}) like the third-order dispersion, the self-steepening, and the self-frequency shift play important roles in the study of the ultra-short optical pulse…
In this paper, a Hirota method is developed for applying to the nonlinear Schr\"odinger equation with arbitrary time-dependent linear potential which denotes the dynamics of soliton solutions in quasi-one-dimensional Bose-Einstein…