Journal of Nonlinear Mathematical Physics

We consider the general Liénard-type equation u¨=∑k=0nfku˙k for n ≥ 4. This equation naturally admits the Lie symmetry ∂∂t. We completely characterize when this equation admits another Lie symmetry, and give an easily verifiable condition for this on the functions f0,..., fn. Moreover, we give an equivalent...

In this paper, we present all constant solutions of the Yang-Mills equations with SU(2) gauge symmetry for an arbitrary constant non-Abelian current in Euclidean space ℝn of arbitrary finite dimension n. Using the invariance of the Yang-Mills equations under the orthogonal transformations of coordinates...

The existence of a new type of cusped solitary wave, which decays algebraically at infinity, for a nonlinear equation modeling the free surface evolution of moderate amplitude waves in shallow water is established by employing qualitative analysis for differential equations. Furthermore, the exact parametric...

The paper is concerned with different classes of nonlinear Klein–Gordon and telegraph type equations with variable coefficients c(x)utt+d(x)ut=[a(x)ux]x+b(x)ux+p(x)f(u), where f(u) is an arbitrary function. We seek exact solutions to these equations by the direct method of symmetry reductions using...

Sklyanin’s formula provides a set of canonical spectral coordinates on the standard Calogero-Moser space associated with the quiver consisting of a vertex and a loop. We generalize this result to Calogero-Moser spaces attached to cyclic quivers by constructing rational functions that relate spectral...

We study a particular class of Lotka-Volterra 3-dimensional systems called May-Leonard systems, which depend on two real parameters a and b, when a + b = −1. For these values of the parameters we shall describe its global dynamics in the compactification of the non-negative octant of ℝ3 including its...

A generalization of the Landau-Lifschitz equation with uniaxial anisotropy is proposed, which can also reduce to the derivative nonlinear Schrödinger equation under an infinitesimal parameter. Based on the gauge transformation between Lax pairs, an N-fold generalized Darboux transformation is constructed...

A class of n-dimensional Poisson systems reducible to an unperturbed harmonic oscillator shall be considered. In such case, perturbations leaving invariant a given symplectic leaf shall be investigated. Our purpose will be to analyze the bifurcation phenomena of periodic orbits as a result of these perturbations...

In this paper, the Hirota bilinear equation of the constrained modified KP hierarchy is expressed as the vacuum expectation values of Clifford operators by using the free fermions method of mKP hierarchy. Then we mainly use the Boson-Fermion correspondence to solve the Hirota bilinear equation of the...

Construction of new integrable systems and methods of their investigation is one of the main directions of development of the modern mathematical physics. Here we present an approach based on the study of behavior of roots of functions of canonical variables with respect to a parameter of simultaneous...

By employing a novel generalization of the inverse scattering transform method known as the unified transform or Fokas method, it can be shown that the solution of certain physically significant boundary value problems for the elliptic sine-Gordon equation, as well as for the elliptic version of the...