A new periodic wave solution in terms of theta functions is presented for a kind of elliptic equation.Based on the results,with the help of Mathematica and the improved generalized F-expansion method,some periodic wave solutions in terms of theta functions are obtained for the(2+1)-dimensional breaking soliton equation.In addition,x-direction periodic wave solutions are derived,their properties and profiles are displayed in 3D figures.To our knowledge,these solutions are reported for the first time.
With the aid of Mathematica,three auxiliary equations,i.e.the Riccati equation,the Lenard equation and the Hyperbolic equation,are employed to investigate traveling wave solutions of a cosh-Gaussian laser beam in both Kerr and cubic quintic nonlinear media.As a result,many traveling wave solutions are obtained,including soliton-like solutions,hyperbolic function solutions and trigonometric function solutions.
