相关论文: Notes on solutions in Wronskian form to soliton eq…
A class of "elliptic soliton" solutions of the Kadomtsev-Petviashvili hierarchy, which includes a determinantal solution of Li and Zhang, is described in terms of pseudo-differential operator formulation. In our approach, the Li-Zhang…
We introduce the most general version of Dubrovin-type equations for divisors on a hyperelliptic curve of arbitrary genus, and provide a new argument for linearizing the corresponding completely integrable flows. Detailed applications to…
Recently proposed nonholonomic deformation of the KdV equation is solved through inverse scattering method by constructing AKNS-type Lax pair. Exact and explicit N-soliton solutions are found for the basic field and the deforming function…
In this paper, we use only the equation of motion for an interacting system of gravity, dilaton and antisymmetric tensor to study the soliton solutions by making use of a Poincar\'e invariant ansatz. We show that the system of equations are…
In the present work, we investigate the soliton structure of the Vakhnenko equation with a 'dissipative' term, by means of the Hirota's method. As a result, we unearth three kinds of soliton solutions depending upon the dissipation…
The bi-Hamiltonian structure is established for the perturbation equations of KdV hierarchy and thus the perturbation equations themselves provide also examples among typical soliton equations. Besides, a more general bi-Hamiltonian…
A variable-coefficient forced Korteweg-de Vries equation with spacial inhomogeneity is investigated in this paper. Under constraints, this equation is transformed into its bilinear form, and multi-soliton solutions are derived. Effects of…
We demonstrate that commuting quasilinear systems of Jordan block type are parametrised by solutions of the modified KP hierarchy. Systems of this form naturally occur as hydrodynamic reductions of multi-dimensional linearly degenerate…
In this paper, we obtain some new explicit travelling wave solutions of the perturbed KdV equation through recent factorization techniques that can be performed when the coefficients of the equation fulfill a certain condition. The…
In this paper we study multivariate kinetic-type equations in a general setup, which includes in particular the spatially homogeneous Boltzmann equation with Maxwellian molecules, both with elastic and inelastic collisions. Using a…
Exact stationary soliton solutions of the fifth order KdV type equation $$ u_t +\alpha u^p u_x +\beta u_{3x}+\gamma u_{5x} = 0$$ are obtained for any p ($>0$) in case $\alpha\beta>0$, $D\beta>0$, $\beta\gamma<0$ (where D is the soliton…
We prove local in time well-posedness for a class of quasilinear Hamiltonian KdV-type equations with periodic boundary conditions, more precisely we show existence, uniqueness and continuity of the solution map. We improve the previous…
The elliptic Korteweg-de Vries (KdV) system is a multi-component generalization of the lattice potential KdV equation, whose soliton solutions are associated with an elliptic Cauchy kernel (i.e., a Cauchy kernel on the torus). In this paper…
Bosonization approach to the classical supersymmetric systems is presented. By introducing the multi-fermionic parameters in the expansions of the superfields, the $\mathcal {N}=1$ supersymmetric KdV (sKdV) equations are transformed to a…
This paper concerns a kinetic model of the thermostated Boltzmann equation with a linear deformation force described by a constant matrix. The collision kernel under consideration includes both the Maxwell molecule and general hard…
A Hamiltonian approach to the solution of the Vlasov-Poisson equations has been developed. Based on a nonlinear canonical transformation, the rapidly oscillating terms in the original Hamiltonian are transformed away, yielding a new…
It is shown that the $N$-dark soliton solutions of the integrable discrete nonlinear Schr\"odinger (IDNLS) equation are given in terms of the Casorati determinant. The conditions for reduction, complex conjugacy and regularity for the…
We give a family of solutions of Witten-Dijkgraaf-Verlinde-Verlinde equations in $n$-dimensional space. It is defined in terms of $BC_{n}$ root system and $n+2$ independent multiplicity parameters. We also apply these solutions to define…
In this paper we present the applications of methods from wavelet analysis to polynomial approximations for a number of accelerator physics problems. In the general case we have the solution as a multiresolution expansion in the base of…
Inspired by the forms of delay-Painleve equations, we consider some new differential-discrete systems of KdV, mKdV and Sine-Gordon - type related by simple one way Miura transformations to classical ones. Using Hirota bilinear formalism we…