In this paper, variable coefficients Kawahara equation (VCKE) and variable coefficients
modified Kawahara equation (VCMKE), which arise in modeling of various physical …

We prove that the initial value problem (IVP) associated to the fifth-order KdV equation\begin
{equation*}\tag {0.1}\partial _tu-\partial^ 5_x u= c_1\partial _xu\partial _x^ 2u+ c_2\partial _x …

In this paper, the Lie symmetry analysis is performed on the fifth-order KdV types of
equations which arise in modeling many physical phenomena. The similarity reductions and …

This paper concerns the initial-boundary value problem of the Kawahara equation posed on
the right and left half-lines. We prove the local well-posedness in the low regularity Sobolev …

The Kawahara equation has fewer symmetries than the KdV equation; in particular, it has no
invariant scaling transform and is not completely integrable. Thus its analysis requires …

We consider the Cauchy problem for the Kawahara equation, which is a fifth-order KdV
equation. This paper establishes the local well-posedness with initial data given in the …

The Cauchy problem for a Korteweg–deVries equation with dispersion of order m= 2 j+ 1,
where j is a positive integer,(KdVm), is studied with data in Sobolev and analytic spaces …

In this manuscript, we consider the internal control problem for the fifth‐order KdV type
equation, commonly called the Kawahara equation, on unbounded domains. Precisely …

Higher order KdV type equations are the equation replaced by a higher order derivative x^
2k+ 1 for the KdV equation. Recently, the local well-posedness result for these equations on …

In this work, we focus on obtaining the exact solutions of the fifth-order semi-linear and non-
linear dispersive partial differential equations, which have the second-order diffusion-like …