Results 21 to 30 of about 292 (78)
Results in Physics, 2021 We introduce a new stochastic robust solver to solve several classes of nonlinear stochastic partial differential equations (NSPDEs). This solver presents the closed formula for the stochastic solutions.
Yousef F. Alharbi +2 more
doaj
Semi–analytical and numerical simulations of the modified Benjamin–Bona–Mahony model
Journal of Ocean Engineering and Science, 2022 In this article, semi-analytical and numerical simulations of the well-known modified Benjamin–Bona–Mahony (mBBM) equation are processed. This study targets to check the accuracy of the obtained analytical solutions of the mBBM model that have been ...
Mostafa M.A. Khater, Samir A. Salama
doaj
Boussinesq’s equation for water waves: the soliton resolution conjecture for Sector IV
Advanced Nonlinear StudiesWe consider the Boussinesq equation on the line for a broad class of Schwartz initial data relevant for water waves. In a recent work, we identified ten main sectors describing the asymptotic behavior of the solution, and for each of these sectors we ...
Charlier Christophe, Lenells Jonatan
doaj +1 more source
Alexandria Engineering Journal, 2023 In this article, we discuss various solitary wave solutions that are extremely important in applied mathematics. In order to construct accurate solution to nonlinear fractional PDEs, we have employed the Khater technique to nonlinear equation for 3 ...
Asghar Ali, Jamshad Ahmad, Sara Javed
doaj
Tropical spectral curves, Fay's trisecant identity, and generalized ultradiscrete Toda lattice [PDF]
, 2010 We study the generalized ultradiscrete periodic Toda lattice T(M,N) which has tropical spectral curve. We introduce a tropical analogue of Fay's trisecant identity, and apply it to construct a general solution to T(M,N).
arxiv +1 more source
Soliton Fay identities. I. Dark soliton case [PDF]
Journal of Physics A, 47 (2014) 415202, 2014 We derive a set of bilinear identities for the determinants of the matrices that have been used to construct the dark soliton solutions for various models. To give examples of the application of the obtained identities we present soliton solutions for the equations describing multidimensional quadrilateral lattices, Darboux equations and ...
arxiv +1 more source
Alexandria Engineering Journal, 2021 This research is based on three main pillars which are studying the computational solutions of the modified Benjamin–Bona–Mahony (BBM) equation via the modified Khater method then investigating the stability property of the obtained solutions through the
Mostafa M.A. Khater +4 more
doaj
Exact solutions of the Gerdjikov-Ivanov equation using Darboux transformations [PDF]
Journal of Nonlinear Mathematical Physics, 22:1, 32-46,2015, 2015 We study the Gerdjikov-Ivanov (GI) equation and present a standard Darboux transformation for it. The solution is given in terms of quasideterminants. Further, the parabolic, soliton and breather solutions of the GI equation are given as explicit examples.
arxiv +1 more source
Ain Shams Engineering Journal, 2021 This research explores the complex and physical behavior, using four different theoretical methods, of water wave propagation with surface tension. A modern Benneye-Luke (BL) algorithm is used to identify a variety of unobtained distinct wave solution ...
Mostafa M.A. Khater +3 more
doaj
Soliton Fay identities. II. Bright soliton case [PDF]
Journal of Physics A, 48 (2015) 445204, 2015 We present a set of bilinear matrix identities that generalize the ones that have been used to construct the bright soliton solutions for various models. As an example of an application of these identities, we present a simple derivation of the N-bright soliton solutions for the Ablowitz-Ladik hierarchy.
arxiv +1 more source