On the continuum limit for a semidiscrete Hirota equation
نویسندگان
چکیده
منابع مشابه
On solutions to the non-Abelian Hirota–Miwa equation and its continuum limits
In this paper, we construct Grammian-like quasideterminant solutions of a non-Abelian Hirota–Miwa equation. Through continuum limits of this non-Abelian Hirota–Miwa equation and its quasideterminant solutions, we construct a cascade of noncommutative differential-difference equations ending with the non-commutative KP equation. For each of these systems, the quasideterminant solutions are const...
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The Hirota–Miwa equation (also known as the discrete KP equation, or the octahedron recurrence) is a bilinear partial difference equation in three independent variables. It is integrable in the sense that it arises as the compatibility condition of a linear system (Lax pair). The Hirota–Miwa equation has infinitely many reductions of plane wave type (including a quadratic exponential gauge tran...
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We present a hermitian matrix chain representation of the general solution of the Hirota bilinear difference equation of three variables. In the large N limit this matrix model provides some explicit particular solutions of continuous differential Hirota equation of three variables. A relation of this representation to the eigenvalues of transfer matrices of 2D quantum integrable models is disc...
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We address the question of the uniqueness of solution to the initial value problem associated to the equation ∂tu+ iα∂ 2 xu+ β∂ 3 xu+ iγ|u| 2 u+ δ|u|∂xu+ ǫu 2 ∂xu = 0, x, t ∈ R, and prove that a certain decay property of the difference u1 − u2 of two solutions u1 and u2 at two different instants of times t = 0 and t = 1, is sufficient to ensure that u1 = u2 for all the time.
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ژورنال
عنوان ژورنال: Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
سال: 2016
ISSN: 1364-5021,1471-2946
DOI: 10.1098/rspa.2016.0628