Semilinear stochastic evolution equations with multiplicative Poisson noise and monotone nonlinear drift in Hilbert spaces are considered‎. ‎The coefficients are assumed to have linear growth‎. ‎We do not impose coercivity conditions on coefficients‎. ‎A novel method of proof for establishing existence and uniqueness of the mild solution is proposed‎. ‎Examples on stochastic partial differentia...

The ultimate topic to be touched on in this book is the vast and active field of nonlinear partial differential equations. Leaving aside quantum mechanics, which remains to date an inherently linear theory, most real-world physical systems, including gas dynamics, fluid mechanics, elasticity, relativity, ecology, neurology, thermodynamics, and many more, are modeled by nonlinear partial differe...

in this paper, first the properties of one and two-dimensional differential transforms are presented.next, by using the idea of differential transform, we will present a method to find an approximate solution fora volterra integro-partial differential equations. this method can be easily applied to many linear andnonlinear problems and is capable of reducing computational works. in some particu...

a simple new closed form of the green function for axisymmetric magnetostatic problemsis found analytically in cylindrical coordinates. the result is verified by applying several examples.

in this paper, a high-order and conditionally stable stochastic difference scheme is proposed for the numerical solution of $rm ithat{o}$ stochastic advection diffusion equation with one dimensional white noise process. we applied a finite difference approximation of fourth-order for discretizing space spatial derivative of this equation. the main properties of deterministic difference schemes,...

The homogeneous balance method can be used to construct exact traveling wave solutions of nonlinear partial differential equations. In this paper, this method is used to construct new soliton solutions of the (3+1) Jimbo--Miwa equation.

In this work, we extend the existing local fractional Sumudu decomposition method to solve the nonlinear local fractional partial differential equations. Then, we apply this new algorithm to resolve the nonlinear local fractional gas dynamics equation and nonlinear local fractional Klein-Gordon equation, so we get the desired non-differentiable exact solutions. The steps to solve the examples a...

In this manuscript, we investigate solutions of the partial differential equations (PDEs) arising inmathematical physics with local fractional derivative operators (LFDOs). To get approximate solutionsof these equations, we utilize the reduce differential transform method (RDTM) which is basedupon the LFDOs. Illustrative examples are given to show the accuracy and reliable results. Theobtained ...