Using the standard truncated Painlevé analysis approach, we have obtained some new special types of multisoliton solutions of a (2+ 1)-dimensionM integrable model, the modified Kadomtsev-Petviashvili (mKP) equation.
From the variable separation solution and by selecting appropriate functions, a new class of localized coherent structures consisting of solitons in various types are found in the (2+1)-dimensional long-wave-short-wav...From the variable separation solution and by selecting appropriate functions, a new class of localized coherent structures consisting of solitons in various types are found in the (2+1)-dimensional long-wave-short-wave resonance interaction equation. The completely elastic and non-elastic interactive behavior between the dromion and compacton, dromion and peakon, as well as between peakon and compacton are investigated. The novel features exhibited by these new structures are revealed for the first time.展开更多
Based on the extended mapping deformation method and symbolic computation, many exact travelling wave solutions are found for the (3+1)-dimensional JM equation and the (3+1)-dimensional KP equation. The obtained solut...Based on the extended mapping deformation method and symbolic computation, many exact travelling wave solutions are found for the (3+1)-dimensional JM equation and the (3+1)-dimensional KP equation. The obtained solutions include solitary solution, periodic wave solution, rational travelling wave solution, and Jacobian and Weierstrass function solution, etc.展开更多
In this paper, the variable separation approach is used to obtain localized coherent structures of the (2+1)-dimensional generalized Davey-Stewarson equations: iqt + 1/2(qxx + qyy) + (R+ S)q = O, Rx=-σ/2|q|2y Sy = -...In this paper, the variable separation approach is used to obtain localized coherent structures of the (2+1)-dimensional generalized Davey-Stewarson equations: iqt + 1/2(qxx + qyy) + (R+ S)q = O, Rx=-σ/2|q|2y Sy = -σ/2|q|2/x.Applying a special Backlund transformation and introducing arbitrary functions of the seed solutions, an abundance of the localized structures of this model is derived. By selecting the arbitrary functions appropriately, some special typesof localized excitations such as dromions, dromion lattice, breathers, and instantons are constructed.展开更多
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,...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.展开更多
Using the variable separation approach, many types of exact solutions of the generalized (2+1)-dimensional Nizhnik-Novikov-Veselov equation are derived. One of the exact solutions of this model is analyzed to study th...Using the variable separation approach, many types of exact solutions of the generalized (2+1)-dimensional Nizhnik-Novikov-Veselov equation are derived. One of the exact solutions of this model is analyzed to study the interaction between a line soliton and a y-periodic soliton.展开更多
Considering that the multi-valued (folded) localized excitations may appear in many (2+1)-dimensional soliton equations because some arbitrary functions can be included in the exact solutions, we use some special type...Considering that the multi-valued (folded) localized excitations may appear in many (2+1)-dimensional soliton equations because some arbitrary functions can be included in the exact solutions, we use some special types of muliti-valued functions to construct folded solitrary waves and foldons in the (2+1)-dimensional Broer-Kaup equation.These folded excitations are invesigated both analytically and graphically in an alternative way.展开更多
文摘Using the standard truncated Painlevé analysis approach, we have obtained some new special types of multisoliton solutions of a (2+ 1)-dimensionM integrable model, the modified Kadomtsev-Petviashvili (mKP) equation.
文摘From the variable separation solution and by selecting appropriate functions, a new class of localized coherent structures consisting of solitons in various types are found in the (2+1)-dimensional long-wave-short-wave resonance interaction equation. The completely elastic and non-elastic interactive behavior between the dromion and compacton, dromion and peakon, as well as between peakon and compacton are investigated. The novel features exhibited by these new structures are revealed for the first time.
文摘Based on the extended mapping deformation method and symbolic computation, many exact travelling wave solutions are found for the (3+1)-dimensional JM equation and the (3+1)-dimensional KP equation. The obtained solutions include solitary solution, periodic wave solution, rational travelling wave solution, and Jacobian and Weierstrass function solution, etc.
文摘In this paper, the variable separation approach is used to obtain localized coherent structures of the (2+1)-dimensional generalized Davey-Stewarson equations: iqt + 1/2(qxx + qyy) + (R+ S)q = O, Rx=-σ/2|q|2y Sy = -σ/2|q|2/x.Applying a special Backlund transformation and introducing arbitrary functions of the seed solutions, an abundance of the localized structures of this model is derived. By selecting the arbitrary functions appropriately, some special typesof localized excitations such as dromions, dromion lattice, breathers, and instantons are constructed.
文摘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.
文摘Using the variable separation approach, many types of exact solutions of the generalized (2+1)-dimensional Nizhnik-Novikov-Veselov equation are derived. One of the exact solutions of this model is analyzed to study the interaction between a line soliton and a y-periodic soliton.
文摘Considering that the multi-valued (folded) localized excitations may appear in many (2+1)-dimensional soliton equations because some arbitrary functions can be included in the exact solutions, we use some special types of muliti-valued functions to construct folded solitrary waves and foldons in the (2+1)-dimensional Broer-Kaup equation.These folded excitations are invesigated both analytically and graphically in an alternative way.
