We introduce an extension of the l-reduced KP hierarchy, which we call the lBogoyavlensky hierarchy. Bogoyavlensky’s 2 + 1-dimensional extension of the KdV equation is the lowest equation of the hierarchy in case of l = 2. We present a group-theoretic characterization of this hierarchy on the basis of the 2-toroidal Lie algebra sl l . This reproduces essentially the same Hirota bilinear equatio...

General breather solution to the Sasa–Satsuma equation (SSE) is systematically investigated in this paper. We firstly transform SSE into a set of three Hirota bilinear equations under proper plane wave boundary condition. Starting from specially arranged tau-function Kadomtsev–Petviashvili hierarchy and 11 satisfied, we implement series steps reduction procedure, i.e. C-type reduction, dimensio...

We investigate symmetries and reductions of a coupled KdV system with variable coefficients. The infinitesimals of the group of transformations which leaves the KdV system invariant and the admissible forms of the coefficients are obtained using the generalized symmetry method based on the Fréchet derivative of the differential operators. An optimal system of conjugacy inequivalent subgroups is...

We consider a class of fully nonlinear Fermi-Pasta-Ulam (FPU) lattices, consisting of a chain of particles coupled by fractional power nonlinearities of order α>1. This class of systems incorporates a classical Hertzian model describing acoustic wave propagation in chains of touching beads in the absence of precompression. We analyse the propagation of localized waves when α is close to unity. ...

We study the travelling wave solutions for a system of coupled KdV equations derived by Lou et al [11]. In that paper, they found 5 types of Painlevé integrable systems for the coupled KdV system. We show that each of them can be reduced to a partially or completely uncoupled system, through which the dynamical behavior of travelling wave solutions can be determined. In some parameter regions, ...

The overtaking collisional phenomenon of slow shear Alfvén solitons are studied in a low beta (β = kinetic pressure/magnetic pressure) collisionless, magnetized plasma consisting electron and ion fluids. By employing reductive perturbation technique, the Korteweg–de Vries (KdV) equation is deduced for investigating nonlinear wave. Before embarking on study collisions, stability analysis KdV usi...

We study the traveling wave solutions for a system of coupled KdV equations derived by Lou et al [11]. In that paper, they found 5 types of Painlevé integrable systems for the coupled KdV system. We show that each of them can be reduced to a partially or completely uncoupled system, through which the dynamical behavior of traveling wave solutions can be determined. In some parameter regions, ex...

He’s variational iteration method [1, 2], which is a modified general Lagrange multiplier method [3], has been shown to solve effectively, easily and accurately a large class of nonlinear problems with approximations which converge quickly to accurate solutions. It was successfully applied to autonomous ordinary differential equations [4], nonlinear partial differential equations with variable ...