Modified homogeneous balance methods (MHBMs)First-order riccati equation with single polynomial termSecond-order riccati equationA combination of the first-order riccati equation and a second-order riccati equa
Methods Appl. (2018) MironovA.E. et al. Some algebraic examples of Frobenius manifolds Theoret. Math. Phys. (2007) GesztesyF. Quasi-periodic, finite-gap solutions of the modified Korteweg–de Vries equationView more references Cited by (9) Multiple localized nonlinear waves of a forced ...
arXiv:1406.3784v1 [physics.flu-dyn] 14 Jun 2014Observation of the Inverse Energy Cascadein the modif i ed Korteweg–de Vries EquationD. Dutykh † and E. Tobisch ∗†LAMA, UMR 5127 CNRS, Universit´ e de Savoie,Campus Scientif i que, 73376 Le Bourget-du-Lac Cedex, France∗ In...
The initial-boundary value problem (ibvp) for a coupled system of modified Korteweg-de Vries (mKdV) equations depending on a parameterαis studied on the half-line. It is shown that this system is well-posed for initial data(u0,v0)(x)in spatial Sobolev spacesHs(0,∞)×Hs(0,∞),s>1...
Khare A, Cooper F (1993) One-parameter family of soliton solutions with compact support in a class of generalized Korteweg–de Vries equation. Phys Rev E 48(6):4843–4 ADSGoogle Scholar Dodan K (2005) An application for the higher order modified KdV equation by decomposition method. Commun...
Klaus Brauer: The Korteweg - de Vries Equation 3 (1) (2) Using the typical short denotations as the problem can be formulated as: This is the Korteweg-de Vries Equation (KdV) which is nonlinear because of the product shown in the second summand and which is of third order because of ...
The stability of cnoidal wavetrain solutions of the modified Korteweg-de Vries equation is analyzed using Whitham's modulational theory. The cnoidal waves are solutions of an oscillator equation obtained by twice integrating the modified Korteweg-de Vries equation. The stability of the cnoidal waves ...
In this paper, we investigate the higher-order modified Korteweg–de Vries (mKdV) equation by using an algebraic method. On the background of the Jacobi elliptic function, we obtain the admissible eigenvalues and the corresponding non-periodic eigenfunctions of the spectral problem in this higher-...
On the basis of the inverse scattering transformation, the Cauchy problem of the coupled modified Korteweg–de Vries equation is transformed to a 3 × 3 matrix Riemann–Hilbert problem. Two distinct factorizations of the jump matrix for the Riemann–Hilbert problem and a decomposition of the vector...
In this paper, we conduct a series of numerical experiments of the interaction between a soliton and a breather in the framework of the modified Korteweg–de Vries equation for different initial wave phases. The structure of the work is as follows. The exact breather and soliton solutions of ...