WebThis paper proposes a new class of arbitrarily high-order conservative numerical schemes for the generalized Korteweg--de Vries (KdV) equation. This approach is based on the scalar auxiliary variable method. The equation is reformulated into an equivalent system by introducing a scalar auxiliary variable, and the energy is reformulated into a sum of two … WebThe Korteweg–de Vries equation \\[ u_t + uu_x + u_{xxx} = 0\\] is a nonlinear partial differential equation arising in the study of a number of different physical systems, e.g., …
Nonlinear small data scattering for the generalized Korteweg-de Vries ...
Web1 de mai. de 1990 · Abstract. We study the longtime stability of small solutions to the IVP for the generalized Korteweg-de Vries equation. We obtain a lower bound for the degrees of nonlinearity of the perturbation which guarantees that the small solutions of the nonlinear problem behave asymptotically like the solutions of the associated linear problem. WebWe show for the Korteweg-de Vries equation an existence uniqueness theorem in Sobolev spaces of arbitrary fractional order s ≧2, provided the initial data is given in the … eado loft apartments
Dispersive Equations and Nonlinear Waves: Generalized Korteweg …
Web5 de nov. de 1996 · Recent numerical simulations of the generalized Korteweg—de Vries equation u t + u p u x + u xxx = 0 indicate that for p⩾4, smooth solutions of the initial-value problem may form singularities in finite time. It is the purpose of this paper to ascertain what effect dissipation has on the instability of solitary waves and the associated blow-up … WebProceedings of the American Mathematical Society. Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics. ISSN 1088-6826 (online) ISSN 0002-9939 (print) WebS. Oh, Resonant phase-shift and global smoothing of the periodic Korteweg–de Vries equation in low regularity settings, Adv. Differential Eq. 18(7–8) (2013) 633–662. Google Scholar; 30. J. Shatah, Normal forms and quadratic nonlinear Klein–Gordon equations, Comm. Pure Appl. Math. 38 (1985) 685–696. Crossref, ISI, Google Scholar; 31. V. ea dodgeball