A Series of Variable Separation Solutions and New Soliton Structures of （2＋1）-Dimensional Korteweg-de Vries Equation

Variable separation approach is introduced to solve the （2＋1）-dimensional KdV equation. A series of variable separation solutions is derived with arbitrary functions in system. We present a new soliton excitation model （24）. Based on this excitation, new soliton structures such as the multi-lump soliton and periodic soliton are revealed by selecting the arbitrary function appropriately.     

Study on （2＋1）-Dimensional Nizhnik-Novikov-Veselov Equation by Using Extended Mapping Approach

Extended mapping approach is introduced to solve （2＋1）-dimensional Nizhnik-Novikov Veselov equation. A new type of variable separation solutions is derived with arbitrary functions in the model. Based on this excitation, rich localized structures such as multi-lump soliton and ring soliton are revealed by selecting the arbitrary function appropriately.     

Two Classes of New Exact Solutions to （2＋1）-Dimensional Breaking Soliton Equation

The singular manifold method is used to obtain two general solutions to a （2＋1）-dimensional breaking soliton equation, each of which contains two arbitrary functions. Then the new periodic wave solutions in terms of the Jacobi elliptic functions are generated from the general solutions. The long wave limit yields the new types of dromion and solitary structures.     

Exotic Localized Coherent Structures of New（2＋1）－Dimensional Soliton Equation

The variable separation approach is used to obtain localized coherent structures of the new(2 1)-dimensional nonlinear partial differential equation.Applying the Baecklund transformation and introducing the arbitrary functions of the seed solutions,the abundance of the localized structures of this model are derived.Some special types of solutions solitoff,dromions,dromion lattice,breathers and instantons are discussed by selecting the arbitrary functions appropriately .The breathers may breath in their amplititudes,shapes,distances among the peaks and even the number of the peaks.     

Dromion and Multi—soliton Structures of the （2＋1）—Dimensional Higher—Order Broer—Kaup System

Using the standard truncated Painleve analysis and the Backlund transformation,we can obtain many significant exact soliton solutions of the (2 1)-dimensional higher-order Broer-Kaup(HBK) system.A special type of soliton solution is described by the variable coefficient heat-conduction-liker equation.The inclusion of three arbitrary functions in the general expressions of the solitons makes the solitons of the (2 1)-dimensional HBK system possess abundant structures such as solitoff solutions,multi-dromion solutions,ring solitons and so on.     

ABUNDANT DROMION-LIKE STRUCTURES TO THE (2+1) DIMENSIONAL KdV EQUATION

The abundant generalized dromion structures for the (2+1)-dimensional KdV equation are obtained using the homogeneous balance method. We give not only the general curve soliton which is finite on a curved line and localized apart from the curve, find but also the dromion solutions which can be driven by two perpendicular line soliton and by two non-perpendicular line soliton and by one line soliton and one curve line soliton. Various types of multi-dromion solutions can be constituted by selecting different arbitrary functions of y. The (1+N) dromion obtained by Radha et al.^[3] is only a very special case of our results.     

New Exact Solutions and Localized Structures for （3＋1）-Dimensional Burgers System

With an extended mapping approach and a linear variable separation method, new families of variable separation solutions （including solitary wave solutions, periodic wave solutions, and rational function solutions） with arbitrary functions for （3＋1）-dimensionai Burgers system is derived. Based on the derived excitations, we obtain some novel localized coherent structures and study the interactions between solitons.     

Variable Separation Solution for （1＋1）-Dimensional Nonlinear Models Related to Schroedinger Equation

A variable separation approach is proposed and successfully extended to the (1 1)-dimensional physics models. The new exact solution of (1 1)-dimensional nonlinear models related to Schr6dinger equation by the entrance of three arbitrary functions is obtained. Some special types of soliton wave solutions such as multi-soliton wave solution,non-stable soliton solution, oscillating soliton solution, and periodic soliton solutions are discussed by selecting the arbitrary functions appropriately.     

Solitons and Waves in （2＋l）-Dimensional Dispersive Long-Wave Equation

For a higher-dimensional integrable nonlinear dynamical system, there are abundant coherent soliton excitations. With the aid of an improved projective Riccati equation approach, the paper obtains several types of exact solutions to the （2＋l）-dimenslonal dispersive long-wave equation, including multiple-soliton solutions, periodic soliton solutions, and Weierstrass function solutions. From these solutions, apart from several multisoliton excitations, we derive some novel features of wave structures by introducing some types of lower-dimensional patterns.     

New Exact Solutions for （1 ＋ 1）-Dimensional Dispersion-Less System

Using improved homogeneous balance method, we obtain complex function form new exact solutions for the （1＋1）-dimensional dispersion-less system, and from the exact solutions we derive real function form solution of the field u. Based on this real function form solution, we find some new interesting coherent structures by selecting arbitrary functions appropriately.     

Deformed two-dimensional rogue waves in the (2+1)-dimensional Korteweg–de Vries equation

Within the(2+1)-dimensional Korteweg–de Vries equation framework,new bilinear B¨acklund transformation and Lax pair are presented based on the binary Bell polynomials and gauge transformation.By introducing an arbitrary functionφ(y),a family of deformed soliton and deformed breather solutions are presented with the improved Hirota’s bilinear method.By choosing the appropriate parameters,their interesting dynamic behaviors are shown in three-dimensional plots.Furthermore,novel rational solutions are generated by taking the limit of the obtained solitons.Additionally,twodimensional(2D)rogue waves(localized in both space and time)on the soliton plane are presented,we refer to them as deformed 2D rogue waves.The obtained deformed 2D rogue waves can be viewed as a 2D analog of the Peregrine soliton on soliton plane,and its evolution process is analyzed in detail.The deformed 2D rogue wave solutions are constructed successfully,which are closely related to the arbitrary functionφ(y).This new idea is also applicable to other nonlinear systems.     

Control of soliton characteristics of the condensate by an arbitrary x-dependent external potential

This paper presents a family of soliton solutions of the one-dimensional nonlinear Schrdinger equation which describes the dynamics of the dark solitons in Bose-Einstein condensates with an arbitrary x-dependent external potential.The obtained results show that the external potential has an important effect on the dark soliton dynamical characteristics of the condensates.The amplitude,width,and velocity of the output soliton are relative to the source position of the external potential.The smaller the amplitude of the soliton is,the narrower its width is,and the slower the soliton propagates.The collision of two dark solitons is nearly elastic.     

Variable separation solutions and new solitary wave structures to the （l＋l）-dimensional Ito system

A variable separation approach is proposed and extended to the (1+1)-dimensional physics system. The variable separation solution of (1+1)-dimensional Ito system is obtained. Some special types of solutions such as non-propagating solitary wave solution, propagating solitary wave solution and looped soliton solution are found by selecting the arbitrary function appropriately.     

Variable separation solutions and new solitary wave structures to the (1+1)-dimensional equations of long-wave－short-wave resonant interaction

A variable separation approach is proposed and extended to the (1+1)-dimensional physical system. The variable separation solutions of (1+1)-dimensional equations of long-wave－short-wave resonant interaction are obtained. Some special type of solutions such as soliton solution, non-propagating solitary wave solution, propagating solitary wave solution, oscillating solitary wave solution are found by selecting the arbitrary function appropriately.     

Exact solutions for the coupled Klein-Gordon-Schrǒdinger equations using the extended F-expansion method

The extended F-expansion method or mapping method is used to construct exact solutions for the coupled KleinGordon Schr/Sdinger equations （K-G-S equations） by the aid of the symbolic computation system Mathematica. More solutions in the Jacobi elliptic function form are obtained, including the single Jacobi elliptic function solutions, combined Jacobi elliptic function solutions, rational solutions, triangular solutions, soliton solutions and combined soliton solutions.     

A Novel Class of Coherent Localized Structures for the Maccari System

By means of the Baecklund transformation, a quite general variable separation solution of the (2 1)-dimensional Maccari systems is derived. In addition to some types of the usual localized excitations such as dromion, lumps, ring soliton and oscillated dromion, breathers solution, fractal-dromion, fractal-lump and chaotic soliton structures can be easily constructed by selecting the arbitrary functions appropriately, a new novel class of coherent localized structures like peakon solution and compacton solution of this new system are found by selecting apfropriate functions.     

Generalized Dromion Structures of New（2＋1）—Dimensional Nonlinear Evolution Equation

We derive the generalized dromions of the new(2 1)-dimensional nonlinear evolution equation by the arbitrary function presented in the bilinearized linear equations.The rich soliton and dromion structures for this system are released.     

New Coherent Structures in the Generalized（2＋1）—Dimensional Nizhnik—Novikov—Veselov System

In high dimensions there are abundant coherent soliton excitations.From the known variable separation solutions for the generalized(2 1)-dimensional Nizhnik-Novikov-Veselov system.two kinds of new coherent structures in this system are obtained.Some interesting novel features of these structures are revealed.     

Objective Reduction Solutions to Higher-Order Boussinesq System in （2＋1）-Dimensions

With the help of an objective reduction approach （ORA）, abundant exact solutions of （2＋1）-dimensional higher-order Boussinesq system （including some hyperboloid function solutions, trigonometric function solutions, and a rational function solution） are obtained. It is shown that some novel soliton structures, like single linearity soliton structure, breath soliton structure, single linearity y-periodic solitary wave structure, libration dromion structure, and kink-like multisoliton structure with actual physical meaning exist in the （2＋1）-dimensional higher-order Boussinesq system.     

Rational and Periodic Wave Solutions of Two-Dimensional Boussinesq Equation

Two new exact, rational and periodic wave solutions are derived for the two-dimensional Boussinesq equation. For the first solution it is obtained by performing an appropriate limiting procedure on the soliton solutions obtained by Hirota bilinear method. The second one in terms of Riemann theta function is explicitly presented by virtue of Hirota bilinear method and its asymptotic property is also analyzed in detail. Moreover, it is of interest to note that classical soliton solutions can be reduced from the periodic wave solutions.