Bäcklund Transformation and Several Types of KdV Equations
نویسندگان
چکیده
منابع مشابه
existence and approximate $l^{p}$ and continuous solution of nonlinear integral equations of the hammerstein and volterra types
بسیاری از پدیده ها در جهان ما اساساً غیرخطی هستند، و توسط معادلات غیرخطی بیان شده اند. از آنجا که ظهور کامپیوترهای رقمی با عملکرد بالا، حل مسایل خطی را آسان تر می کند. با این حال، به طور کلی به دست آوردن جوابهای دقیق از مسایل غیرخطی دشوار است. روش عددی، به طور کلی محاسبه پیچیده مسایل غیرخطی را اداره می کند. با این حال، دادن نقاط به یک منحنی و به دست آوردن منحنی کامل که اغلب پرهزینه و ...
15 صفحه اولBäcklund transformations for several cases of a type of generalized KdV equation
An alternate generalized Korteweg-de Vries system is studied here. A procedure for generating solutions is given. A theorem is presented, which is subsequently applied to this equation to obtain a type of Bäcklund transformation for several specific cases of the power of the derivative term appearing in the equation. In the process, several interesting, new, ordinary, differential equations are...
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15 صفحه اولBäcklund Transformation for the Krichever-novikov Equation
The Krichever-Novikov equation u t = u xxx − 3 2u x (u 2 xx − r(u)) + cu x , r (5) = 0 (1) appeared (up to change u = p(˜ u), ˙ p 2 = r(p)) in [1] for the first time in connection with study of finite-gap solutions of the Kadomtsev-Petviashvili equation. The distinctive feature of the equation (1) is that, accordingly to [2], no differential substitution exists connecting it with other KdV-type...
متن کاملCanonicity of Bäcklund transformation : r - matrix approach .
For the Hamiltonian integrable systems governed by SL(2)-invariant r-matrix (such as Heisenberg magnet, Toda lattice, nonlinear Schrödinger equation) a general procedure for constructing Bäcklund transformation is proposed. The corresponding BT is shown to preserve the Poisson bracket. The proof is given by a direct calculation using the r-matrix expression for the Poisson bracket.
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ژورنال
عنوان ژورنال: Pure Mathematics
سال: 2018
ISSN: 2160-7583,2160-7605
DOI: 10.12677/pm.2018.82015