In this paper, the coupled dispersive (2+1)-dimensional long wave equation is studied. The traveling wave hypothesis yields complexiton solutions. Subsequently, the wave equation is studied with power law nonlinearity where the ansatz method is applied to yield solitary wave solutions. The constraint conditions for the existence of solitons naturally fall out of the derivation of the soliton so...

the purpose of this paper is to analyze in detail a special nonlinear partial differentialequation (npde) of the second order which is important in physical, chemical and technicalapplications. the present npde describes nonlinear diffusion and is of interest in several partsof physics, chemistry and engineering problems alike. since nature is not linear intrinsicallythe nonlinear case is there...

We present a general algorithm to show that a scattering operator associated to a semilinear dispersive equation is real analytic, and to compute the coefficients of its Taylor series at any point. We illustrate this method in the case of the Schrödinger equation with powerlike nonlinearity or with Hartree type nonlinearity, and in the case of the wave and Klein–Gordon equations with power nonl...

A generalization of the Hopf–Cole transformation and its relation to the Burgers equation of integer order and the diffusion equation with quadratic nonlinearity are discussed. The explicit form of a particular analytical solution is presented. The existence of the travelling wave solution and the interaction of nonlocal perturbation are considered. The nonlocal generalizations of the one-dimen...

piezoelectric microcantilevers (mcs) are a new generation of microbeams used in atomic force microscopes (afms). due to their miniaturization of afms as well as their increased imaging precision and speed, these mcs are more popular than their classical counterparts. given the widespread application of these beams in nanoparticle topography, analysis of their vibrating motion has attracted much...

Acoustic wave propagation in ultrasonic flow measurements is typically assumed to be linear and reciprocal. However, if the transmitting transducer generates a sufficiently high pressure, nonlinear effects become significant. In measurements, this would translate into more information estimate therefore higher precision relative case. work, we investigate how generated harmonics can used measur...

in this paper, the coupled dispersive (2+1)-dimensional long wave equation is studied. the traveling wave hypothesis yields complexiton solutions. subsequently, the wave equation is studied with power law nonlinearity where the ansatz method is applied to yield solitary wave solutions. the constraint conditions for the existence of solitons naturally fall out of the derivation of the soliton so...

In the present short communication, we revisit nonlinearity management of the timeperiodic nonlinear Schrödinger equation and the related averaging procedure. By means of rigorous estimates, we show that the averaged nonlinear Schrödinger equation does not blow up in the higher dimensional case so long as the corresponding solution remains smooth. In particular, we show that the H norm remains ...

The global existence in time for nonlinear wave equation with small data usually require high Sobolev regularity, when one dealt with them by classical energy method (see [Kl85] [Ch85]). The purpose of this note is to give the sharp regularity global existence for semilinear equation with the power nonlinearity of the derivative, the counterpart of quasilinear equation or the quadratic nonlinea...