Continuous limits for an integrable coupling system of Toda equation hierarchy

In this Letter, we present an integrable coupling system of lattice hierarchy and its continuous limits by using of Lie algebra sl(4). By introducing a complex discrete spectral problem, the integrable coupling system of Toda lattice hierarchy is derived. It is shown that a new complex lattice spectral problem converges to the integrable couplings of discrete soliton equation hierarchy, which has the integrable coupling system of C-KdV hierarchy as a new kind of continuous limit.     

New positon, negaton and complexiton solutions for the Bogoyavlensky-Konoplechenko equation

New positon, negaton and complexiton solutions for the Bogoyavlensky-Konoplechenko equation are constructed by means of the Darboux transformation with constant seed solution. The new positon, negaton and complexiton solutions are analytical or singular and given out both analytically and graphically.     

Inverse Scattering Method and Soliton Solution Family for String Effective Action

A modified Hauser-Ernst-type linear system is established and used to develop an inverse scattering method for solving the motion equations of the string effective action describing the coupled gravity, dilaton and KalbRamond fields. The reduction procedures in this inverse scattering method are found to be fairly simple, which makes the proposed inverse scattering method applied fine and effective. As an application, a concrete family of soliton solutions for the considered theory is obtained.     

Soliton-like solutions of certain types of nonlinear diffusion-reaction equations with variable coefficient

With a view to exploring new soliton-like solutions of certain types of nonlinear diffusion-reaction (DR) equations with a variable coefficient, we demonstrate the viability of a method which is the combination of both the symbolic computation technique of Gao and Tian [Y.T. Gao, B. Tian, Comput. Phys. Commun. 133 (2001) 158] and auxiliary equation method of Sirendaoreji [Sirendaoreji, Phys. Lett. A 356 (2006) 124] and used recently for the KdV equation. In particular, the DR equations with quadratic and cubic nonlinearities with a time-dependent velocity in the convective flux term are studied and the existence of soliton-like solutions is shown.     

A new extended KP hierarchy

A method is proposed to construct a new extended KP hierarchy, which includes two types of KP equation with self-consistent sources and admits reductions to k-constrained KP hierarchy and to Gelfand-Dickey hierarchy with sources. It provides a general way to construct soliton equations with sources and their Lax representations.     

On the solutions of 3-particle spin elliptic Calogero-Moser systems

We describe a class of the singular solutions to the multicomponent analogs of the Lamé equation, arising as equations of motion of the elliptic Calogero-Moser systems of particles carrying spin 1/2. At special value of the coupling constant we propose the ansatz which allows one to get meromorphic solutions with two arbitrary parameters. They are quantized upon the requirement of the regularity of the wave function on the hyperplanes at which particles meet and imposing periodic boundary conditions. We find also the extra integrals of motion for three-particle systems which commute with the Hamiltonian for arbitrary values of the coupling constant.     

The double Wronskian solutions of a non-isospectral Kadomtsev-Petviashvili equation

The double Wronskian solutions of a non-isospectral Kadomtsev-Petviashvili equation (n-KPE) are derived. One-soliton solution and two-soliton solution are presented, the characteristics of one-soliton and two-soliton scattering are discussed also.     

Grammian Solutions to a Variable-Coefficient KP Equation

Solutions in the Grammian form for a variable-coefficient Kadomtsev-Petviashvili （KP） equation which has the Wronskian solutions are derived by means of Pfaffian derivative formulae.     

R-Matrix of the Coupling AKNS Equation Hierarchy

A new r-matrix of the integrable coupling system is obtained by nonlineaxization of the coupling eigenvalue problem. As a reduction, we present the r-matrix of the coupling Ablowitz-Kaup Newell Segur （AKNS） equation hierarchy via enlarged matrix Lie algebra.     

Exact Bosonic Solutions of the Truncated Skyrme Model

A model defined by half the Lagrangian （the highly nonlinear part） of the Skyrme model is investigated. Two classes of bosonic solutions are obtained. It is shown that, although the field configurations of these two classes are different, the energy densities for the two classes take the same form.