Maximal function estimates of solutions to general dispersive partial differential equations

Topological soliton solutions of the some nonlinear partial differential equations

In this paper, we obtained the 1-soliton solutions of the symmetric regularized long wave (SRLW) equation and the (3+1)-dimensional shallow water wave equations. Solitary wave ansatz method is used to carry out the integration of the equations and obtain topological soliton solutions The physical parameters in the soliton solutions are obtained as functions of the dependent coefficients. Note t...

Global Estimates for Solutions of Partial Differential Equations∗

For a polynomial P (ξ) in ξ in R with constant complex coefficients, the operator defined by R(z)f = F((P (·)−z)f̂), where ∧ denotes the Fourier transform and F denotes its inverse, is not bounded from L to L when z is in the spectrum of P (D). What are suitable spaces B and C so that R(z) is bounded from B to C? When P (ξ) is simply characteristic, we prove that the operator R(z) is bounded fro...

Some L* Estimates for Partial Differential Equations

to hold for functions u satisfying given (possibly void) boundary conditions, where the Ak are linear partial differential operators, p is greater than one, and || • j | , , 3 , is an L p norm defined for all real values of 5. When 5 is a non-negative integer, ||w||8fl, is essentially the sum of the L norms of u and all its derivatives up to order s. We do not require that the A * be of the sam...

topological soliton solutions of the some nonlinear partial differential equations

in this paper, we obtained the 1-soliton solutions of the symmetric regularized long wave (srlw) equation and the (3+1)-dimensional shallow water wave equations. solitary wave ansatz method is used to carry out the integration of the equations and obtain topological soliton solutions the physical parameters in the soliton solutions are obtained as functions of the dependent coefficients. note t...

Some Estimates on Exponentials of Solutions to Stochastic Differential Equations