The paper is concerned with Lp error analysis of semi-discrete Galerkin FEMs for nonlinear parabolic equations. The classical energy approach relies heavily on the strong regularity assumption of the diffusion coefficient, which may not be satisfied in many physical applications. Here we focus our attention on a general nonlinear parabolic equation (or system) in a convex polygon or polyhedron ...

A wide range of nonlinear optical coefficients and various systems of notation have been used to describe optical second-harmonic generation (5MG). To avoid possible confusion, the techniques of optical nonlinear coefficient measurement and the elementary theory of SHG are briefly reviewed. Absolute and relative nonlinear coefficient measurements by phase-matched SHG are described. The followin...

We study both theoretically and experimentally the nonlinear interaction between an intense surface acoustic wave and a two-dimensional electron plasma in semiconductor-piezocrystal hybrid structures. The experiments on hybrid systems exhibit strongly nonlinear acoustoelectric effects. The plasma turns into moving electron stripes, the acoustoelectric current reaches its maximum, and the sound ...

A normal form is derived for Hamiltonian–Hopf bifurcations of solitary waves in nonlinear Schrödinger equations with general external potentials. This normal form is a simple second-order nonlinear ordinary differential equation (ODE) that is asymptotically accurate in describing solution dynamics near Hamiltonian–Hopf bifurcations. When the nonlinear coefficient in this normal form is complex,...

To the theory of quasi-phase-matched parametric amplification in periodically-poled optical nonlinear crystals Abstract Theory of the optical parametric amplification at high-frequency pumping in crystals with a regular space modulation of the sign of nonlinear coupling coefficient of interacting waves is developed. By applying the matrix method, the theory is based on a step-by-step approach. ...

In this paper, we use two different integral techniques, the first integral and the direct integral method, to study the variable coefficient nonlinear Schrödinger (NLS) equation arising in arterial mechanics. The application of the first integral method yielded periodic and solitary wave solutions. Using the direct integration lead to solitary wave solution and Jacobi elliptic function solutions.

This study is related to inverse coefficient problems for a nonlinear parabolic variational inequality with an unknown leading coefficient in the equation for the gradient of the solution. An inverse method, involving minimization of a least-squares cost functional, is developed to identify the unknown coefficient. It is proved that the solution of the corresponding direct problem depends conti...

We report the bright solitons of the generalized Gross-Pitaevskii (GP) equation with some types of physically relevant parity-time- ( PT-) and non- PT-symmetric potentials. We find that the constant momentum coefficient Γ can modulate the linear stability and complicated transverse power-flows (not always from the gain toward loss) of nonlinear modes. However, the varying momentum coefficient Γ...

In this Letter, we propose a generic nonlinear coupling coefficient, η(NL)²=η|γ/β₂|(fiber2)/|γ/β₂|(fiber1), which gives a quantitative measure for the efficiency of nonlinear matching of optical fibers by describing how a fundamental soliton couples from one fiber into another. Specifically, we use η(NL) to demonstrate a significant soliton self-frequency shift of a fundamental soliton, and we ...

We consider the problem of identifying an unknown coefficient in a onedimensional diffusion equation from overspecified data measured in the interior of the domain. We obtain an identifiability result which is used to derive a uniqueness result for the inverse problem.