This work investigates a nonlocal sinh-Gordon equation with singularly perturbed parameter in ball. Under the Robin boundary condition, solution asymptotically forms quite steep layer thin annular region, and rapidly becomes flat curve outside this region. {Focusing more particularly on structure of pointwise asymptotic expansion involving domain-size is evaluated sharply, where exactly appears...

In this paper, we consider the Cauchy problem for Klein-Gordon equation with a cubic convolution nonlinearity in R. Making use of Bourgain’s method in conjunction with precise Strichartz estimates of S.Klainerman and D.Tataru, we establish the Hs-global well-posedness with s < 1 of the Cauchy problem for the cubic convolution defocusing Klein-Gordon-Hartree equation, inspired by I. Gallagher an...

The matrix sine-Gordon theory, a matrix generalization of the well-known sine-Gordon theory, is studied. In particular, the A3-generalization where fields take value in SU(2) describes integrable deformations of conformal field theory corresponding to the coset SU(2)× SU(2)/SU(2). Various classical aspects of the matrix sine-Gordon theory are addressed. We find exact solutions, solitons and bre...

in this work g&apos;/g-expansion method has been employed to solve (2+1)-dimensional dispersive long wave equation. it is shown that g&apos;/g-expansion method, with the help of symbolic computation, provides a very effective and powerful mathematical tool, for solving this equation.

in the present work‎, ‎a new stochastic algorithm is proposed to solve multiple dimensional fredholm integral equations of the second kind‎. ‎the solution of the‎ integral equation is described by the neumann series expansion‎. ‎each term of this expansion can be considered as an expectation which is approximated by a continuous markov chain monte carlo method‎. ‎an algorithm is proposed to sim...

In this article we will develop some techniques aimed at the strong couplings in two-dimensional wave-Klein-Gordon system. We distinguish roles of different type decay factors and a method which permits us to “exchange” one into other. Then global existence result model problem is established. also give sketch Klein-Gordon-Zakharov system establish associate result.

The Wiener process was used to explore the (2 + 1)-dimensional chiral nonlinear Schrödinger equation (CNLSE). This model outlines energy characteristics of quantum physics’ fractional Hall effect edge states. sine-Gordon expansion technique (SGET) implemented extract stochastic solutions for CNLSE through multiplicative noise effects. method accurately described a variety solitary behaviors, in...