Stability and instability of standing-wave solutions to one-dimensional quadratic-cubic Klein–Gordon equations

Rational Solutions of Pairs of Diagonal Equations, One Cubic and One Quadratic

We obtain an essentially optimal estimate for the moment of order 32/3 of the exponential sum having argument αx + βx. Subject to modest local solubility hypotheses, we thereby establish that pairs of diagonal Diophantine equations, one cubic and one quadratic, possess nontrivial integral solutions whenever the number of variables exceeds 10.

Complexition and solitary wave solutions of the (2+1)-dimensional dispersive long wave equations

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...

Stability and instability of standing waves for nonlinear Schrödinger equations

Orthogonal stability of mixed type additive and cubic functional equations

In this paper, we consider orthogonal stability of mixed type additive and cubic functional equation of the form $$f(2x+y)+f(2x-y)-f(4x)=2f (x+y)+2f(x-y)-8f(2x) +10f(x)-2f(-x),$$ with $xbot y$, where $bot$  is orthogonality in the sense of Ratz.

complexition and solitary wave solutions of the (2+1)-dimensional dispersive long wave equations

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...