We investigate the Cauchy problem for a nonlocal (two-place) FORQ equation. By interpreting this equation as special case of two-component peakon system (exhibiting cubic nonlinearity), we convert into ordinary differential equations in Banach space. Using approach, are able to demonstrate local well-posedness Sobolev space Hs where s>5/2. also establish continuity properties data-to-solution m...

Nonlinear partial differential equations are widely used to describe complex phenomena in various fields of science, for example the Korteweg-de Vries-Kuramoto-Sivashinsky equation (KdV-KS equation) and the Ablowitz-Kaup-Newell-Segur shallow water wave equation (AKNS-SWW equation). To our knowledge the exact solutions for the first equation were still not obtained and the obtained exact solutio...

(Received 25 June 1998, revised version received 05 January 1999) The Lax pair for a derivative nonlinear Schrödinger equation proposed by Chen-Lee-Liu is generalized into matrix form. This gives new types of integrable coupled derivative nonlinear Schrödinger equations. By virtue of a gauge transformation, a new multi-component extension of a derivative nonlinear Schrödinger equation proposed ...

We consider the use of rational basis functions to compute scattering and inverse transforms associated with AKNS (Ablowitz–Kaup–Newell–Segur) system. The proposed numerical forward transform computes solution system that is valid on entire real axis thereby a reflection coefficient at point by solving single linear makes novel improvement in function approach oscillatory Cauchy operator, enabl...

The string equation appearing in the double scaling limit of the Hermitian one–matrix model, which corresponds to a Galilean self–similar condition for the KdV hierarchy, is reformulated as a scaling self–similar condition for the Ur–KdV hierarchy. A non–scaling limit analysis of the one–matrix model has led to the complexified NLS hierarchy and a string equation. We show that this corresponds ...

در این پژوهش تقویت باریکه لیزر تپی فمتوثانیه Ti:sapphire ­کننده بازتولیدی با آرایش هندسی Z براساس روش تپ چیرپ بررسی شده است. برای انتقال ورودی اولیه به داخل کاواک و استخراج از دو سلول پاکل استفاده زمان شکل‌گیری برحسب انرژی دمش مطالعه روند تحول مورد قرار گرفته مدت تولید بدون حضور 80 نانوثانیه فرایند 38 نرخ تکرار 10 هرتز طول موج مرکزی 800 نانومتر بیشینه 2 میلی‌ژول بعد 17 رفت برگشت 15 میلی ژول 532...

We introduce and study an integrable boundary flow possessing an infinite number of conserving charges which can be thought of as quantum counterparts of the Ablowitz, Kaup, Newell and Segur Hamiltonians. We propose an exact expression for overlap amplitudes of the boundary state with all primary states in terms of solutions of certain ordinary linear differential equation. The boundary flow is...