Related papers: A two-component nonlinear variational wave system
Floating offshore structures often exhibit low-frequency oscillatory motions in the horizontal plane, with amplitudes in the same order as their characteristic dimensions and larger than the corresponding wave-frequency responses, making…
The question of a possible excitation and emergence of fractional type dynamics, as a more realistic framework for understanding emergence of complex systems, directly from a conventional integral order dynamics, in the form a continuous…
We consider two-component integrable generalizations of the dispersionless 2DTL hierarchy connected with non-Hamiltonian vector fields, similar to the Manakov-Santini hierarchy generalizing the dKP hierarchy. They form a one-parametric…
We consider the asymptotic behaviour of small-amplitude gravity water waves in a rectangular domain where the water depth is much smaller than the horizontal scale. The control acts on one lateral boundary, by imposing the horizontal…
The interest in the Camassa-Holm equation inspired the search for various generalizations of this equation with interesting properties and applications. In this letter we deal with such a two-component integrable system of coupled…
In this paper, we study the bilinear form and the general N-soliton solution for a two-component Hunter-Saxton (2-HS) equation, which is the short wave limit of a twocomponent Camassa-Holm equation. By defining a hodograph transformation…
In this paper, we consider initial-boundary value problems for two-component nonlinear systems of time-fractional diffusion equations with the homogeneous Neumann boundary condition and non-negative initial values. The main results are the…
Extending previous results of Oh--Zumbrun and Johnson--Zumbrun, we show that spectral stability implies linearized and nonlinear stability of spatially periodic traveling-wave solutions of viscous systems of conservation laws for systems of…
Governing equations for two-dimensional inviscid free-surface flows with constant vorticity over arbitrary non-uniform bottom profile are presented in exact and compact form using conformal variables. An efficient and very accurate…
A Hamiltonian model for the propagation of internal water waves interacting with surface waves, a current and an uneven bottom is examined. Using the so-called Dirichlet-Neumann operators, the water wave system is expressed in the…
In the present study we consider three two-component (integrable and non-integrable) systems which describe the propagation of shallow water waves on a constant shear current. Namely, we consider the two-component Camassa-Holm equations,…
We recently introduced a particular nonlinear generalization of quantum mechanics which has the property that it is exactly solvable in terms of the eigenvalues and eigenfunctions of the Hamiltonian of the usual linear quantum mechanics…
This paper considers a pair of coupled nonlinear Helmholtz equations \begin{align*} -\Delta u - \mu u = a(x) \left( |u|^\frac{p}{2} + b(x) |v|^\frac{p}{2} \right)|u|^{\frac{p}{2} - 2}u, \end{align*} \begin{align*} -\Delta v - \nu v = a(x)…
We analyze two-component spatial optical vortex solitons supported by parametric wave mixing processes in a nonlinear bulk medium. We study two distinct cases of such localised waves, namely, parametric vortex solitons due to phase-matched…
We develop a complete stability theory for two-dimensional periodic traveling waves of reaction-diffusion systems. More precisely, we identify a diffusive spectral stability assumption, prove that it implies nonlinear stability and provide…
In this note, we announce a general result resolving the long-standing question of nonlinear modulational stability, or stability with respect to localized perturbations, of periodic traveling-wave solutions of the generalized…
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…
We prove the existence of nonlinear normal modes for general systems of two coupled nonlinear oscillators. Facilitating the comparison principle for ordinary differential equations it is shown that there exist exact solutions representing a…
We present a novel general framework to deal with forward and backward components of the electromagnetic field in axially-invariant nonlinear optical systems, which include those having any type of linear or nonlinear transverse…
We introduce two-parameter classes of exactly-solvable novel systems whose Hamiltonian operators could be represented by tridiagonal symmetric matrices in some orthogonal bases. The associated wavefunction is written as point-wise…