The higher-order Kaup-Newell equation is examined by applying the Fokas unified method on the half-line.We demonstrate that the solution can be expressed in relation to the resolution of the Riemann-Hilbert problem.Th...The higher-order Kaup-Newell equation is examined by applying the Fokas unified method on the half-line.We demonstrate that the solution can be expressed in relation to the resolution of the Riemann-Hilbert problem.The jump matrix for this problem is derived from the spectral matrix,which is calculated based on both the initial conditions and the boundary conditions.The jump matrix is explicitly dependent and expressed through the spectral functions,which are derived from the initial and boundary information,respectively.These spectral functions are interdependent and adhere to a so-called global relationship.展开更多
In this paper, the Fokas unified method is used to analyze the initial-boundary value problem of a complex Sharma–Tasso–Olver(c STO) equation on the half line. We show that the solution can be expressed in terms of ...In this paper, the Fokas unified method is used to analyze the initial-boundary value problem of a complex Sharma–Tasso–Olver(c STO) equation on the half line. We show that the solution can be expressed in terms of the solution of a Riemann–Hilbert problem. The relevant jump matrices are explicitly given in terms of the matrix-value spectral functions spectral functions {a(λ), b(λ)} and {A(λ), B(λ)}, which depending on initial data u_0(x) = u(x, 0) and boundary data g_0(y) = u(0, y), g_1(y) = ux(0, y), g_2(y) = u_(xx)(0, y). These spectral functions are not independent, they satisfy a global relation.展开更多
In this paper,we apply Fokas unified method to study the initial boundary value(IBV)problems for nonlinear integrable equation with 3×3 Lax pair on the finite interval[0,L].The solution can be expressed by the so...In this paper,we apply Fokas unified method to study the initial boundary value(IBV)problems for nonlinear integrable equation with 3×3 Lax pair on the finite interval[0,L].The solution can be expressed by the solution of a 3×3 Riemann-Hilbert(RH)problem.The relevant jump matrices are written in terms of matrix-value spectral functions s(k),S(k),S_(l)(k),which are determined by initial data at t=0,boundary values at x=0 and boundary values at x=L,respectively.What's more,since the eigenvalues of 3×3 coefficient matrix of k spectral parameter in Lax pair are three different values,search for the path of analytic functions in RH problem becomes a very interesting thing.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
文摘The higher-order Kaup-Newell equation is examined by applying the Fokas unified method on the half-line.We demonstrate that the solution can be expressed in relation to the resolution of the Riemann-Hilbert problem.The jump matrix for this problem is derived from the spectral matrix,which is calculated based on both the initial conditions and the boundary conditions.The jump matrix is explicitly dependent and expressed through the spectral functions,which are derived from the initial and boundary information,respectively.These spectral functions are interdependent and adhere to a so-called global relationship.
基金Supported by National Natural Science Foundation of China under Grant Nos.11271008 and 61072147
文摘In this paper, the Fokas unified method is used to analyze the initial-boundary value problem of a complex Sharma–Tasso–Olver(c STO) equation on the half line. We show that the solution can be expressed in terms of the solution of a Riemann–Hilbert problem. The relevant jump matrices are explicitly given in terms of the matrix-value spectral functions spectral functions {a(λ), b(λ)} and {A(λ), B(λ)}, which depending on initial data u_0(x) = u(x, 0) and boundary data g_0(y) = u(0, y), g_1(y) = ux(0, y), g_2(y) = u_(xx)(0, y). These spectral functions are not independent, they satisfy a global relation.
基金supported by the National Natural Science Foundation of China(11901167,11971313 and 51879045)Key scientific research projects of higher education institutions in Henan,China(18B110008).
文摘In this paper,we apply Fokas unified method to study the initial boundary value(IBV)problems for nonlinear integrable equation with 3×3 Lax pair on the finite interval[0,L].The solution can be expressed by the solution of a 3×3 Riemann-Hilbert(RH)problem.The relevant jump matrices are written in terms of matrix-value spectral functions s(k),S(k),S_(l)(k),which are determined by initial data at t=0,boundary values at x=0 and boundary values at x=L,respectively.What's more,since the eigenvalues of 3×3 coefficient matrix of k spectral parameter in Lax pair are three different values,search for the path of analytic functions in RH problem becomes a very interesting thing.
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.
