Lou Sen-Yue

Interactions Between Solitons and Cnoidal Periodic Waves of the Boussinesq Equation

The Boussinesq equation is one of important prototypic models in nonlinear physics. Various nonlinear excitations of the Boussinesq equation have been found by many methods. However, it is very difficult to find interaction solutions among different types of nonlinear excitations. In this peper, two equivalent very simple methods, the truncated Painleve analysis and the generalized tanh function expansion approaches, are developed to find interaction solutions between solitons and any other types of Boussinesq waves.

Darboux Transformations via Lie Point Symmetries: KdV Equation

By localizing the nonlocal symmetries of a nonlinear model to local symmetries of an enlarged system, we find Darboux-Backlund transformations for both the original and prolonged systems. The idea is explicitly realized for the well-known KdV equation.

Interactions between Solitons and Cnoidal Periodic Waves of the Gardner Equation

The Gardner equation is one of the most important prototypic models in nonlinear physics. Many scholars pay much attention to the Gardner equation and various nonlinear excitations of the Gardner equation have been found by many methods. However, it is very difficult to find interaction solutions among different types of nonlinear excitations. In this work, with the help of the Riccati equation, the Gardner equation is solved by the consistent Riccati expansion. Furthermore, we obtain the soliton-cnoidal wave interaction solutions of the Gardner equation.

Interactions among Periodic Waves and Solitary Waves of the (2+1)-Dimensional Konopelchenko?Dubrovsky Equation

By using the truncated Painleve analysis and the generalized tanh function expansion approaches, many interaction solutions among solitons and other types of nonlinear excitations of the Konopelchenko—Dubrovsky (KD) equation can be obtained. Particularly, the soliton-cnoidal wave interaction solutions are studied by means of the Jacobi elliptic functions and the third type of incomplete elliptic integrals.

Nonlocalization of Nonlocal Symmetry and Symmetry Reductions of the Burgers Equation

Symmetry reduction method is one of the best ways to find exact solutions. In this paper, we study the possibility of symmetry reductions of the well known Burgers equation including the nonlocal symmetry. The related new group invariant solutions are obtained. Especially, the interactions among solitons, Airy waves, and Kummer waves are explicitly given.

Bäcklund Transformations and Interaction Solutions of the Burgers Equation

The Burgers equation is one of the most important prototypic models in nonlinear physics. Various exact solutions of the Burgers equation have been found by many methods. However, it is very difficult to find interactive solutions among different types of nonlinear excitations. We develop a generalized tanh function expansion approach, which can be considered as the Backlund transformation, to find interactive solutions between the soliton and other types of Burgers waves.

CRE Method for Solving mKdV Equation and New Interactions Between Solitons and Cnoidal Periodic Waves

In nonlinear physics, the modified Korteweg de-Vries (mKdV) as one of the important equation of nonlinear partial differential equations, its various solutions have been found by many methods. In this paper, the CRE method is presented for constructing new exact solutions. In addition to the new solutions of the mKdV equation, the consistent Riccati expansion (CRE) method can unearth other equations.

Interactions Between Solitons and Cnoidal Periodic Waves of the (2+1)-Dimensional Konopelchenko-Dubrovsky Equation

The (2+1)-dimensional Konopelchenko—Dubrovsky equation is an important prototypic model in nonlinear physics, which can be applied to many fields. Various nonlinear excitations of the (2+1)-dimensional Konopelchenko—Dubrovsky equation have been found by many methods. However, it is very difficult to find interaction solutions among different types of nonlinear excitations. In this paper, with the help of the Riccati equation, the (2+1)-dimensional Konopelchenko—Dubrovsky equation is solved by the consistent Riccati expansion (CRE). Furthermore, we obtain the soliton-cnoidal wave interaction solution of the (2+1)-dimensional Konopelchenko—Dubrovsky equation.

Generalized symmetries of an = 1 supersymmetric Boiti–Leon–Manna–Pempinelli system*

The formal series symmetry approach (FSSA), a quite powerful and straightforward method to establish infinitely many generalized symmetries of classical integrable systems, has been successfully extended in the supersymmetric framework to explore series of infinitely many generalized symmetries for supersymmetric systems. Taking the = 1 supersymmetric Boiti–Leon–Manna–Pempinelli system as a concrete example, it is shown that the application of the extended FSSA to this supersymmetric system leads to a set of infinitely many generalized symmetries with an arbitrary function f (t). Some interesting special cases of symmetry algebras are presented, including a limit case f (t) = 1 related to the commutativity of higher order generalized symmetries.