Integrable systems play a crucial role in physics and mathematics.In particular,the traditional(1+1)-dimensional and(2+1)-dimensional integrable systems have received significant attention due to the rarity of integra...Integrable systems play a crucial role in physics and mathematics.In particular,the traditional(1+1)-dimensional and(2+1)-dimensional integrable systems have received significant attention due to the rarity of integrable systems in higher dimensions.Recent studies have shown that abundant higher-dimensional integrable systems can be constructed from(1+1)-dimensional integrable systems by using a deformation algorithm.Here we establish a new(2+1)-dimensional Chen-Lee-Liu(C-L-L)equation using the deformation algorithm from the(1+1)-dimensional C-L-L equation.The new system is integrable with its Lax pair obtained by applying the deformation algorithm to that of the(1+1)-dimension.It is challenging to obtain the exact solutions for the new integrable system because the new system combines both the original C-L-L equation and its reciprocal transformation.The traveling wave solutions are derived in implicit function expression,and some asymmetry peakon solutions are found.展开更多
In this paper,the N-soliton solutions to the nonlocal reverse space-time Chen-Lee-Liu equation have been derived.Under the nonlocal symmetry reduction to the matrix spectral problem,the nonlocal reverse space-time Che...In this paper,the N-soliton solutions to the nonlocal reverse space-time Chen-Lee-Liu equation have been derived.Under the nonlocal symmetry reduction to the matrix spectral problem,the nonlocal reverse space-time Chen-Lee-Liu equation can be obtained.Based on the spectral problem,the specific matrix Riemann-Hilbert problem is constructed for this nonlocal equation.Through solving this associated Riemann-Hilbert problem,the N-soliton solutions to this nonlocal equation can be obtained in the case of the jump matrix as an identity matrix.展开更多
In this paper, the Fokas unified method is used to analyze the initial-boundary value for the ChenLee-Liu equation i？tu ＋ ？xxu-i｜u2｜？xu = 0 on the half line（-∞, 0] with decaying initial value. Assuming that th...In this paper, the Fokas unified method is used to analyze the initial-boundary value for the ChenLee-Liu equation i？tu ＋ ？xxu-i｜u2｜？xu = 0 on the half line（-∞, 0] with decaying initial value. Assuming that the solution u（x, t） exists, we show that it can be represented in terms of the solution of a matrix Riemann-Hilbert problem formulated in the plane of the complex spectral parameter λ. The jump matrix has explicit（x, t） dependence and is given in terms of the spectral functions{a（λ）, b（λ）}and{A（λ）, B（λ）}, which are obtained from the initial data u0（x） = u（x, 0） and the boundary data g0（t） = u（0, t）, g1（t） = ux（0, t）, respectively. The spectral functions are not independent,but satisfy a so-called global relation.展开更多
The purpose of the current study is to assess the effectiveness and exactness of the new Modification of the Adomian Decomposition (MAD) method in providing fast converging numerical solutions for the Chen-Lee-Liu (CL...The purpose of the current study is to assess the effectiveness and exactness of the new Modification of the Adomian Decomposition (MAD) method in providing fast converging numerical solutions for the Chen-Lee-Liu (CLL) equation. In addition, we are able to simulate the scheme and provide a comparative analysis with the help of some exact soliton solutions in optical fibers. Finally, the MAD method uncovered that the strategy is proven to be reliable due to the elevated level of accuracy and less computational advances, as demonstrated by a series of tables and figures.展开更多
We construct the soliton solution and smooth positon solution of the second-type derivative nonlinear Schr¨odinger(DNLSII) equation. Additionally, we present a detailed discussion about the decomposition of the p...We construct the soliton solution and smooth positon solution of the second-type derivative nonlinear Schr¨odinger(DNLSII) equation. Additionally, we present a detailed discussion about the decomposition of the positon solution, and display its approximate orbits and variable "phase shift". The second and third order breather-positon solutions are also constructed.展开更多
This study investigates the perturbed Chen–Lee–Liu model that represents the propagation of an optical pulse in plasma and optical fiber.The generalized exponential rational function method is used for this purpose....This study investigates the perturbed Chen–Lee–Liu model that represents the propagation of an optical pulse in plasma and optical fiber.The generalized exponential rational function method is used for this purpose.As a result,we obtain some non-trivial solutions such as the optical singular,periodic,hyperbolic,exponential,trigonometric soliton solutions.We aim to express the pulse propagation of the generated solutions,by taking specific values for the free parameters existed in the obtained solutions.The obtained results show that the generalized exponential rational function technique is applicable,simple and effective to get the solutions of nonlinear engineering and physical problems.Moreover,the acquired solutions display rich dynamical evolutions that are important in practical applications.展开更多
基金Project supported by the National Natural Science Foundation of China (Grant Nos.12275144,12235007,and 11975131)K.C.Wong Magna Fund in Ningbo University。
文摘Integrable systems play a crucial role in physics and mathematics.In particular,the traditional(1+1)-dimensional and(2+1)-dimensional integrable systems have received significant attention due to the rarity of integrable systems in higher dimensions.Recent studies have shown that abundant higher-dimensional integrable systems can be constructed from(1+1)-dimensional integrable systems by using a deformation algorithm.Here we establish a new(2+1)-dimensional Chen-Lee-Liu(C-L-L)equation using the deformation algorithm from the(1+1)-dimensional C-L-L equation.The new system is integrable with its Lax pair obtained by applying the deformation algorithm to that of the(1+1)-dimension.It is challenging to obtain the exact solutions for the new integrable system because the new system combines both the original C-L-L equation and its reciprocal transformation.The traveling wave solutions are derived in implicit function expression,and some asymmetry peakon solutions are found.
基金supported by the National Natural Science Foundation of China under Grant No.11975145。
文摘In this paper,the N-soliton solutions to the nonlocal reverse space-time Chen-Lee-Liu equation have been derived.Under the nonlocal symmetry reduction to the matrix spectral problem,the nonlocal reverse space-time Chen-Lee-Liu equation can be obtained.Based on the spectral problem,the specific matrix Riemann-Hilbert problem is constructed for this nonlocal equation.Through solving this associated Riemann-Hilbert problem,the N-soliton solutions to this nonlocal equation can be obtained in the case of the jump matrix as an identity matrix.
基金Supported by the National Natural Science Foundation of China(No.11271008,61072147,11671095)SDUST Research Fund(No.2018TDJH101)
文摘In this paper, the Fokas unified method is used to analyze the initial-boundary value for the ChenLee-Liu equation i？tu ＋ ？xxu-i｜u2｜？xu = 0 on the half line（-∞, 0] with decaying initial value. Assuming that the solution u（x, t） exists, we show that it can be represented in terms of the solution of a matrix Riemann-Hilbert problem formulated in the plane of the complex spectral parameter λ. The jump matrix has explicit（x, t） dependence and is given in terms of the spectral functions{a（λ）, b（λ）}and{A（λ）, B（λ）}, which are obtained from the initial data u0（x） = u（x, 0） and the boundary data g0（t） = u（0, t）, g1（t） = ux（0, t）, respectively. The spectral functions are not independent,but satisfy a so-called global relation.
文摘The purpose of the current study is to assess the effectiveness and exactness of the new Modification of the Adomian Decomposition (MAD) method in providing fast converging numerical solutions for the Chen-Lee-Liu (CLL) equation. In addition, we are able to simulate the scheme and provide a comparative analysis with the help of some exact soliton solutions in optical fibers. Finally, the MAD method uncovered that the strategy is proven to be reliable due to the elevated level of accuracy and less computational advances, as demonstrated by a series of tables and figures.
基金Supported by the National Natural Science Foundation of China under Grant No.11671219the K.C.Wong Magna Fund in Ningbo Universitythe Natural Science Foundation of Zhejiang Province under Grant No.LZ19A010001
文摘We construct the soliton solution and smooth positon solution of the second-type derivative nonlinear Schr¨odinger(DNLSII) equation. Additionally, we present a detailed discussion about the decomposition of the positon solution, and display its approximate orbits and variable "phase shift". The second and third order breather-positon solutions are also constructed.
文摘This study investigates the perturbed Chen–Lee–Liu model that represents the propagation of an optical pulse in plasma and optical fiber.The generalized exponential rational function method is used for this purpose.As a result,we obtain some non-trivial solutions such as the optical singular,periodic,hyperbolic,exponential,trigonometric soliton solutions.We aim to express the pulse propagation of the generated solutions,by taking specific values for the free parameters existed in the obtained solutions.The obtained results show that the generalized exponential rational function technique is applicable,simple and effective to get the solutions of nonlinear engineering and physical problems.Moreover,the acquired solutions display rich dynamical evolutions that are important in practical applications.
