The Broer-Kaup equation is one of many equations describing some phenomena shallow water wave. There are errors in scientific research because the existence non-smooth boundaries. In this paper, we generalize to fractal space and establish variational formulations through semi-inverse method. acquired formulation reveals conservation laws an energy form suggests possible solution structures mor...

We take into account here the stochastic-fractional Broer–Kaup equations (SFBKEs) perturbed by multiplicative Wiener process. To get rational, hyperbolic, and elliptic stochastic solutions for SBKEs, we utilize Jacobi function method. The derived are significantly more useful effective in comprehending various important challenging physical phenomena due to of SFBKEs describing propagation shal...

A construction of the bi-Hamiltonian structures for integrable systems on regular time scales is presented. The trace functional on an algebra of δ-pseudo-differential operators, valid on an arbitrary regular time scale, is introduced. The linear Poisson tensors and the related Hamiltonians are derived. The quadratic Poisson tensors is given by the use of the recursion operators of the Lax hier...

In this paper, based on the fractional Riccati equation, we propose an extended fractional Riccati sub-equation method for solving fractional partial differential equations. The fractional derivative is defined in the sense of the modified Riemann-Liouville derivative. By a proposed variable transformation, certain fractional partial differential equations are turned into fractional ordinary di...

In this paper, the space–time fractional Whitham–Broer–Kaup equations are investigated. By means of new scaling transformations, nonlinear system different time and space orders is transformed to integer one. The multiple solitary solutions periodic obtained, respectively. All those given exactly by introducing which makes our study unique from most existing studies. It expected that exact for ...

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