Higher-order integrable evolution equation and its soliton solutions
نویسنده
چکیده
We consider an extended nonlinear Schrödinger equation with higher-order odd (third order) and even (fourth order) terms with variable coefficients. We demonstrate its integrability, provide its Lax pair, and, applying the Darboux transfromation, present its first and second order soliton solutions. The equation and its solutions have two free parameters. Setting one of these parameters to zero admits two limiting cases: the Hirota equation on the one hand and the Lakshmanan Porsezian Daniel (LPD) equation on the other hand. When both parameters are zero, the limit is the nonlinear Schrödinger equation.
منابع مشابه
Multi soliton solutions, bilinear Backlund transformation and Lax pair of nonlinear evolution equation in (2+1)-dimension
As an application of Hirota bilinear method, perturbation expansion truncated at different levels is used to obtain exact soliton solutions to (2+1)-dimensional nonlinear evolution equation in much simpler way in comparison to other existing methods. We have derived bilinear form of nonlinear evolution equation and using this bilinear form, bilinear Backlund transformations and construction of ...
متن کاملTwo-fold integrable hierarchy of nonholonomic deformation of the DNLS and the Lenells-Fokas equation
The concept of the nonholonomic deformation formulated recently for the AKNS family is extended to the Kaup-Newell class. Applying this construction we discover a novel mixed integrable hierarchy related to the deformed derivative nonlinear Schrödinger (DNLS) equation and found the exact soliton solutions exhibiting unusual accelerating motion for both its field and the perturbing functions. Ex...
متن کاملNew explicit and Soliton Wave Solutions of Some Nonlinear Partial Differential Equations with Infinite Series Method
To start with, having employed transformation wave, some nonlinear partial differential equations have been converted into an ODE. Then, using the infinite series method for equations with similar linear part, the researchers have earned the exact soliton solutions of the selected equations. It is required to state that the infinite series method is a well-organized method for obtaining exact s...
متن کاملN ov 2 00 2 Integrable hierarchy , 3 × 3 constrained systems , and parametric and peaked stationary solutions
This paper gives a new integrable hierarchy of nonlinear evolution equations. The DP equation: mt + umx + 3mux = 0, m = u − uxx, proposed recently by Desgaperis and Procesi [7], is the first one in the negative hierarchy while the first one in the positive hierarchy is: mt = 4(m − 2 3 )x − 5(m − 2 3 )xxx + (m 2 3 )xxxxx. The whole hierarchy is shown Lax-integrable through solving a key matrix e...
متن کاملLie Symmetries, Kac-Moody-Virasoro Algebras and Integrability of Certain (2+1)-Dimensional Nonlinear Evolution Equations
In this paper we study Lie symmetries, Kac-Moody-Virasoro algebras, similarity reductions and particular solutions of two different recently introduced (2+1)-dimensional nonlinear evolution equations, namely (i) (2+1)-dimensional breaking soliton equation and (ii) (2+1)-dimensional nonlinear Schrödinger type equation introduced by Zakharov and studied later by Strachan. Interestingly our studie...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2013