The Cauchy problem for the Kawahara equation with data in analytic Gevrey spaces on circle is considered and its local well-posedness these proved. Using Bourgain-Gevrey type appropriate bilinear estimates, it shown that time wellposedness holds when initial belong to an of order σ. Moreover, solution not necessarily Gσ time. However, belongs G5σ near zero every x circle. We study a . With circ...

A generalization of the KP equation involving higher-order dispersion is studied. This appears in several physical applications. As new results, Lie point symmetries are obtained and used to derive conservation laws via Noether's theorem by introduction a potential which gives Lagrangian formulation for equation. The meaning properties conserved quantities described. Explicit line soliton solut...

This article proposes a numerical algorithm utilizing the spectral Tau method for numerically handling Kawahara partial differential equation. The double basis of fifth-kind Chebyshev polynomials and their shifted ones are used as functions. Some theoretical results in deriving our proposed algorithm. nonlinear term equation is linearized using new product formula with first derivative polynomi...

In this article, we prove that the ⟨p,q⟩ condition holds, first by using Fuchs index of complex Kawahara equation, and then proving all meromorphic solutions equations belong to class W. Moreover, method is employed get equation traveling wave exact equation. Our results reveal rational ur(x+νt) simply periodic us,1(x+νt) are solitary solutions, while us,2(x+νt) not real-valued. Finally, comput...