Related papers: A coupled Volterra system and its exact solutions
The existence of decompositions of the nonlinear integrable systems not only permits us to establish so-called linear superposition solutions but also to derive new nonlinear integrable coupled systems. Restricting our attention to the…
We propose a spectral collocation method, based on the generalized Jacobi wavelets along with the Gauss-Jacobi quadrature formula, for solving a class of third-kind Volterra integral equations. To do this, the interval of integration is…
A new class of integrable two-dimensional dilaton gravity theories, in which scalar matter fields satisfy the Toda equations, is proposed. The simplest case of the Toda system is considered in some detail, and on this example we outline how…
In the framework of the Poisson geometry of twistor space we consider a family of perturbed 3-dimensional Kepler systems. We show that Hamilton equations of this systems are integrated by quadratures. Their solutions for some subcases are…
We investigate the multi-soliton solutions to the generalized discrete KdV equation. In some cases a soliton with smaller amplitude moves faster than that with larger amplitude unlike the soliton solutions of the KdV equation. This…
We derive formulae for the calculation of Taylor coefficients of solutions to systems of Volterra integral equations, both linear and nonlinear, either without singularities or with singularities of Abel type and logarithmic type. We also…
In this paper we present some relevant dynamical properties of a 3D Lotka-Volterra system from the Poisson dynamics point of view.
A nonlocal form of a two-layer fluid system is proposed by a simple symmetry reduction, then by applying multiple scale method to it a general nonlocal two place variable coefficient modified KdV (VCmKdV) equation with shifted space and…
In this manuscript, consideration is given to the existence of periodic traveling-wave solutions to the $abcd$-system. This system was derived by Bona, Saut, and Chen to describe small amplitude, long wavelength gravity waves on the surface…
We propose the algebro-geometric mothod of construction of solutions of the discrete KP equation over a finite field. We also perform the corresponding reduction to the finite field version of the discrete KdV equation. We write down…
A Weierstrass type projective Riccati equation expansion method is proposed by using the Weierstrass elliptic function solutions of the projective Riccati equations and the conversion formulas which transform the Weierstrass elliptic…
It is demonstrated that a standard coupled-mode theory can successfully describe weakly-nonlinear gravity water waves in Bragg resonance with a periodic one-dimensional topography. Analytical solutions for gap solitons provided by this…
The KdV equation can be derived in the shallow water limit of the Euler equations. Over the last few decades, this equation has been extended to include higher order effects. Although this equation has only one conservation law, exact…
We construct a large family of evidently integrable Hamiltonian systems which are generalizations of the KM system. The Hamiltonian vector field is homogeneous cubic but in a number of cases a simple change of variables transforms such a…
This paper presents two new Weierstrass elliptic function solutions of the projective Riccati equations and four conversion formulas for converting the Weierstrass elliptic functions to the hyperbolic and trigonometric functions. The…
We study (2+1)-dimensional multicomponent spatial vector solitons with a nontrivial topological structure of their constituents, and demonstrate that these solitary waves exhibit a symmetry-breaking instability provided their total…
A system of coupled scalar fields is introduced which possesses a spectrum of massive single-soliton solutions. Some of these solutions are unstable and decay into lower mass stable solitons. Some properties of the solutions are obtained…
A new three-dimensional second-order nonlinear wave equation is introduced which passes the Painleve test for integrability and possesses KdV-type multisoliton solutions. Lax integrability of this equation remains unknown.
We study classical solutions (existence, uniqueness, and explicit solution operator) for homogeneous, linear, and semilinear abstract Volterra integral equations of wave type with almost sectorial operators. We use a functional calculus for…
A complete classification of compacton solutions is carried out for a generalization of the Kadomtsev-Petviashvili (KP) equation involving nonlinear dispersion in two and higher spatial dimensions. In particular, precise conditions are…