Initial-boundary value problems for the two-component complex modified Korteweg-de Vries equation on the interval
نویسندگان
چکیده
We apply the Fokas unified method to study initial-boundary value (IBV) problems for two-component complex modified Korteweg-de Vries (mKdV) equation with a $ 4\times 4 Lax pair on interval. The solution can be written by of Riemann-Hilbert (RH) problem constructed in \lambda $-plane. relevant jump matrices are explicitly expressed terms three matrix-valued spectral functions related initial values, and Dirichlet-Neumann boundary respectively. Moreover, we get that these satisfy global relation also asymptotic analysis functions. By considering relation, express unknown values known via Gelfand-Levitan-Marchenko (GLM) representation.
منابع مشابه
Initial-Boundary Value Problems for the Korteweg-de Vries Equation
Exact and approximate solutions of the initial-boundary value problem for the Korteweg-de Vries equation on the semi-infinite line are found. These solutions are found for both constant and time-dependent boundary values. The form of the solution is found to depend markedly on the specific boundary and initial value. In particular, multiple solutions and nonsteady solutions are possible. The an...
متن کاملAn initial-boundary value problem for the Korteweg-de Vries equation on the negative quarter-plane
In this paper, we consider an initial-boundary value problem for the Kortewegde Vries equation on the negative quarter-plane. The normalized Korteweg-de Vries equation considered is given by uτ + uux + uxxx = 0, x < 0, τ > 0, where x and τ represent dimensionless distance and time respectively. In particular, we consider the case when the initial and boundary conditions are given by u(x, 0) = u...
متن کاملThe Initial-boundary Value Problem for the Korteweg-de Vries Equation
We prove local well-posedness of the initial-boundary value problem for the Korteweg-de Vries equation on right half-line, left half-line, and line segment, in the low regularity setting. This is accomplished by introducing an analytic family of boundary forcing operators.
متن کاملGeneral Boundary Value Problems of the Korteweg-de Vries Equation on a Bounded Domain
In this paper we consider the initial boundary value problem of the Korteweg-de Vries equation posed on a finite interval ut + ux + uxxx + uux = 0, u(x, 0) = φ(x), 0 < x < L, t > 0 (0.1) subject to the nonhomogeneous boundary conditions, B1u = h1(t), B2u = h2(t), B3u = h3(t) t > 0 (0.2)
متن کاملThe initial boundary problem for the Korteweg – de Vries equation on the negative quarter - plane
The initial boundary-value problem for the Korteweg–de Vries (KdV) equation on the negative quarter-plane, x < 0 and t > 0, is considered. The formulation of this problem is different to the usual initial boundary-value problem on the positive quarter-plane, for which x > 0 and t > 0. Two boundary conditions are required at x = 0 for the negative quarter-plane problem, in contrast to the one bo...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Discrete and Continuous Dynamical Systems - Series S
سال: 2023
ISSN: ['1937-1632', '1937-1179']
DOI: https://doi.org/10.3934/dcdss.2022111