-
Article
Fourier integral operators on \(L^p({\mathbb {R}}^{n})\) when \(2<p\le \infty \)
In this note we consider a Fourier integral operator \(T_{\phi ,a}\) T ...
-
Article
New exact solutions of some (2+1)-dimensional Burgers-type systems and interactions
In this paper, we construct new exact solutions of some (2+1)-dimensional Burgers-type systems by using corresponding Cole–Hopf-type transformations. The obtained linear equations show that abundant (2+1)-dime...
-
Article
Hardy-Rellich Type Inequalities Associated with Dunkl Operators
In this paper, the authors obtain the Dunkl analogy of classical Lp Hardy inequality for p > N + 2γ with sharp constant $${\left({{{p - N - 2\...
-
Article
Hardy-Poincaré Type Inequalities Related to k-Hessian Operator
In this paper, we obtain some improved Hardy inequalities for Hessian integrals \(I_{p,k}[u,\Omega ]\) I p , k [ u , Ω ] by symmetrization method under conditions that \({\Omega }\) Ω is a bounded...
-
Article
Open AccessA modified complex short pulse equation of defocusing type
In this paper, we are concerned with a modified complex short pulse (mCSP) equation of defocusing type. Firstly, we show that the mCSP equation is linked to a complex coupled dispersionless equation of defocus...
-
Article
Open AccessA class of third-order nonlinear evolution equations admitting invariant subspaces and associated reductions
With the aid of symbolic computation by Maple, a class of third-order nonlinear evolution equations admitting invariant subspaces generated by solutions of linear ordinary differential equations of order less ...
-
Article
Open AccessA note on a class of Hardy-Rellich type inequalities
In this note we provide simple and short proofs for a class of Hardy-Rellich type inequalities with the best constant, which extends some recent results.
-
Article
Maximal dimension of invariant subspaces to systems of nonlinear evolution equations
In this paper, the dimension of invariant subspaces admitted by nonlinear systems is estimated under certain conditions. It is shown that if the two-component nonlinear vector differential operator ...
-
Article
Lie group classification of the N-th-order nonlinear evolution equations
In this paper, Lie group classification to the N-th-order nonlinear evolution equation $$u_t = u_{Nx} + F\left( {x,t,u,u_x , \ldots ...
-
Article
Weighted Hardy and Rellich inequality on Carnot groups
We prove some weighted Hardy and Rellich inequalities on general Carnot groups with weights associated to the norm constructed by Folland’s fundamental solution of the Kohn sub-Laplacian.
-
Article
Lie symmetry analysis and Painlevé analysis of the new (2+1)-dimensional KdV equation
Lie point symmetries associated with the new (2+1)-dimensional KdV equation u t + 3u x ...
-
Article
New periodic solutions of nonlinear evolution equations
In this paper, some new periodic solutions of nonlinear evolution equations and corresponding travelling wave solutions are obtained by using the double function method and Jacobi elliptic functions.
