Related papers: Integrable variant Blaszak-Szum lattice equation

We obtain an exact solution for the breather lattice solution of the modified Korteweg-de Vries (MKdV) equation. Numerical simulation of the breather lattice demonstrates its instability due to the breather-breather interaction. However,…

The generalized perturbative reduction method is used to find the two-component vector breather solution of the Born-Infeld equation $ U_{tt} -C U_{zz} = - A U_{t}^{2} U_{zz} - \sigma U_{z}^{ 2} U_{tt} + B U_{z} U_{t} U_{zt} $. It is shown…

We investigate two-fluid BGK kinetic methods for binary fluids. The developed theory works for asymmetric as well as symmetric systems. For symmetric systems it recovers Sirovich's theory and is summarized in models A and B. For asymmetric…

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…

Inspired by the works of Ablowitz, Mussliman and Fokas, a partial reverse space-time nonlocal Mel'nikov equation is introduced. This equation provides two dimensional analogues of the nonlocal Schrodinger-Boussinesq equation. By employing…

We present a new method in order to get variable slip coefficient in binary lattice Boltzmann models to simulate gaseous flows. Boundary layer theory is presented. We study both the single- and multi-fluid BGK-type models as well. The…

We propose a differential difference equation in ${\mathcal R}^1\times {\mathcal Z}^2$ and study it by Hirota's bilinear method. This equation has a singular continuum limit into a system which admits the reduction to the Davey-Stewartson…

This paper deals with the construction and analysis of two integrators for (semi-linear) second-order partial differential-algebraic equations of semi-explicit type. More precisely, we consider an implicit-explicit Crank-Nicolson scheme as…

In this paper, a variable-coefficient Boiti-Leon-Manna-Pempinelli equation is to be investigated. We obtain abundant multi-wave, breather wave and lump solutions by using the three waves method, the homoclinic breather approach and the…

Solving the Gross--Pitaevskii (GP) equation describing a Bose--Einstein condensate (BEC) immersed in an optical lattice potential can be a numerically demanding task. We present a variational technique for providing fast, accurate solutions…

Under the Flaschka-Newell Lax pair, the Darboux transformation for the Painlev\'{e}-II equation is constructed by the limiting technique. With the aid of the Darboux transformation, the rational solutions are represented by the Gram…

We consider a two-dimensional Fermi-Pasta-Ulam (FPU) lattice with hexagonal symmetry. Using asymptotic methods based on small amplitude ansatz, at third order we obtain a reduction to a cubic nonlinear Schrodinger equation (NLS) for the…

Based on Sirovich's two-fluid kinetic theory and a dodecagonal discrete velocity model, a two-dimensional 61-velocity finite-difference lattice Boltzmann method for the complete Navier-Stokes equations of binary fluids is formulated.…

The lattice Boltzmann method, now widely used for a variety of applications, has also been extended to model multi-phase flows through different formulations. While already applied to many different configurations in the low Weber and…

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…

The lattice Boltzmann method (LBM) has gained increasing popularity in incompressible viscous flow simulations, but it uses many more variables than necessary. This defect was overcome by a recent approach that solves the more actual…

With rheology applications in mind, we present a fast solver for the time-dependent effective viscosity of an infinite lattice containing one or more neutrally buoyant smooth rigid particles per unit cell, in a two-dimensional Stokes fluid…

Using Sklyanin's classical theory of integrable boundary conditions, we use the Hamiltonian approach to derive new integrable boundary conditions for the Ablowitz-Ladik model on the finite and half infinite lattice. In the case of half…

We present several methods, which utilize symplectic integration techniques based on two and three part operator splitting, for numerically solving the equations of motion of the disordered, discrete nonlinear Schr\"odinger (DDNLS)…

We investigate the interaction characteristics of nonlinear coherent structures in the couple Boussinesq (CB) system using the Hirota bilinear approach. First, we derive the lump solutions using a positive quadratic polynomial within the…