In the study of nonlinear physics, the search of new exact solutions of nonlinear evolution equations (NEEs) is one of the most important problems. Various methods for obtaining exact solutions to NEEs have been proposed, such as the Lie group method of infinitesimal transformations [1], the nonclassical Lie group method [2], the Clarkson and Kruskal direct method (CK) [3 – 5], the conditional ...

The (2+1)-dimensional higher-order Broer-Kaup (HBK) system is studied by nonlocal symmetry method and consistent tanh expansion (CTE) method in this paper. Some exact interaction solutions among different nonlinear excitations such as solitons, rational waves, periodic waves and corresponding images are explicitly given. PACS numbers: 02.30.Jr, 11.10.Lm, 02.20.-a, 04.20.Jb

In this paper, the third kind of Darboux transformation of generalized Broer–Kaup equations is derived from the corresponding spectral problem. By virtue of this Darboux transformation, new 2N -soliton solutions with parameters of the generalized Broer–Kaup equations are obtained. Although 2N is an even number, it is graphically shown that in the cases of N= 1 and N = 2 the obtained 2N -soliton...

The interactions between soliton solutions of integrable models are usually considered to be completely elastic. That is to say, the amplitude, velocity and wave shape of solitons are not changed after nonlinear interaction [1]. However, for some specific solutions of some (2+1)-dimensional models, the interactions among solitonic excitations are not completely elastic since their shapes are ch...

We obtain new gauge-invariant forms of two-dimensional integrable systems of nonlinear equations: the Sawada–Kotera and Kaup–Kuperschmidt system, the generalized system of dispersive long waves, and the Nizhnik–Veselov–Novikov system. We show how these forms imply both new and well-known two-dimensional integrable nonlinear equations: the Sawada–Kotera equation, Kaup–Kuperschmidt equation, disp...