相关论文: The Theory of Binary Nonlinearization and Its Appl…

Generally, natural scientific problems are so complicated that one has to establish some effective perturbation or nonperturbation theories with respect to some associated ideal models. In this Letter, a new theory that combines…

A kind of Bargmann symmetry constraints involving Lax pairs and adjoint Lax pairs is proposed for soliton hierarchy. The Lax pairs and adjoint Lax pairs are nonlinearized into a hierarchy of commutative finite dimensional integrable…

The nonlinear equations describing all the nonsingular pencils of metrics of constant Riemannian curvature are derived and the integrability of these nonlinear equations by the method of inverse scattering problem is proved. It is proved…

The control of bilinear systems has attracted considerable attention in the field of systems and control for decades, owing to their prevalence in diverse applications across science and engineering disciplines. Although much work has been…

In contrast to mono-constrained flows with N degrees of freedom, binary constrained flows of soliton equations, admitting 2x2 Lax matrices, have 2N degrees of freedom. By means of the existing method, Lax matrices only yield the first N…

We study bifurcations and spectral stability of solitary waves in coupled nonlinear Schr\"odinger equations (CNLS) on the line. We assume that the coupled equations possess a solution of which one component is identically zero, and call it…

The emergence of confined structures and pattern formation are exceptional manifestations of concurring nonlinear interactions found in a variety of physical, chemical and biological systems[1]. Optical solitons are a hallmark of extreme…

Equilibria of binary neutron stars in close circular orbits are computed numerically in a waveless formulation: The full Einstein-relativistic-Euler system is solved on an initial hypersurface to obtain an asymptotically flat form of the…

Applying the inverse scattering transform to study a focusing two-component Hirota equation with nonzero boundary conditions at infinity. Through the spectral problem and the adjoint spectral problem, the analyticity properties and symmetry…

Nonlinear spectral problems arise across a range of fields, including mechanical vibrations, fluid-solid interactions, and photonic crystals. Discretizing infinite-dimensional nonlinear spectral problems often introduces significant…

Liouville (super)integrability of a Hamiltonian system of differential equations is based on the existence of globally well-defined constants of the motion, while Lie point symmetries provide a local approach to conserved integrals.…

These notes are meant as an introduction to the theory of nonlinear spectral theory. We will discuss the variational form of nonlninear eigenvalue problems and the corresponding non-linear Euler--Lagrange equations, as well as connections…

Binary embedding is the problem of mapping points from a high-dimensional space to a Hamming cube in lower dimension while preserving pairwise distances. An efficient way to accomplish this is to make use of fast embedding techniques…

Many nonlinear optimal control and optimization problems involve constraints that combine continuous dynamics with discrete logic conditions. Standard approaches typically rely on mixed-integer programming, which introduces scalability…

We propose a general algebraic analytic scheme for the spectral transform of solutions of nonlinear evolution equations. This allows us to give the general integrable evolution corresponding to an arbitrary time and space dependence of the…

A non-singular formulation of the boundary integral method (BIM) is presented for the Laplace equation whereby the well-known singularities that arise from the fundamental solution are eliminated analytically. A key advantage of this…

We consider nonlinear effects in scattering of light by a periodic structure supporting optical bound states in the continuum. In the spectral vicinity of the bound states the scattered electromagnetic field is resonantly enhanced…

A class of nonlinear Schr\"odinger equations involving a triad of power law terms together with a de Broglie-Bohm potential is shown to admit symmetry reduction to a hybrid Ermakov-Painlev\'e II equation which is linked, in turn, to the…

This paper is on the effect of nonlinearity in the equations for propagation of disturbances on transition in the class of Spiral Poiseuille Flows. The problem is approached from the fundamental point of view of following the growth of…

This paper is concerned with the cavity scattering problem in an infinite thin plate, where the out-of-plane displacement is governed by the two-dimensional biharmonic wave equation. Based on an operator splitting, the scattering problem is…