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Modified Kortewegde Vries surfaces
, 2008
"... In this work, we consider 2surfaces in R 3 arising from the modified Korteweg de Vries (mKdV) equation. We give a method for constructing the position vector of the mKdV surface explicitly for a given solution of the mKdV equation. mKdV surfaces contain Willmorelike and Weingarten surfaces. We sho ..."
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In this work, we consider 2surfaces in R 3 arising from the modified Korteweg de Vries (mKdV) equation. We give a method for constructing the position vector of the mKdV surface explicitly for a given solution of the mKdV equation. mKdV surfaces contain Willmorelike and Weingarten surfaces. We
On an integrable discretization of the modified Korteweg–de Vries equation
 Phys. Lett. A
, 1997
"... Abstract. We find time discretizations for the two ”second flows ” of the Ablowitz–Ladik hierachy. These discretizations are described by local equations of motion, as opposed to the previously known ones, due to Taha and Ablowitz. Certain superpositions of our maps allow a one–field reduction and s ..."
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Cited by 3 (2 self)
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and serve therefore as valid space–time discretizations of the modified Kortewegde Vries equation. We expect the performance of these discretizations to be much better then that of the Taha–Ablowitz scheme. The way of finding interpolating Hamiltonians for our maps is also indicated, as well
Exact solutions to the modified Kortewegde Vries equation
 Theor. Math. Phys
"... A formula for certain exact solutions to the modified Kortewegde Vries (mKdV) equation is obtained via the inverse scattering transform method. The kernel of the relevant Marchenko integral equation is written with the help of matrix exponentials as Ω(x + y; t) = Ce−(x+y)Ae8A 3tB, where the real m ..."
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Cited by 2 (0 self)
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A formula for certain exact solutions to the modified Kortewegde Vries (mKdV) equation is obtained via the inverse scattering transform method. The kernel of the relevant Marchenko integral equation is written with the help of matrix exponentials as Ω(x + y; t) = Ce−(x+y)Ae8A 3tB, where the real
Group Invariant Solutions of Complex Modified Kortewegde Vries Equation
"... The complex modified Kortewegde Vries (CMKdV) equation which can reduce to modified Kortewegde Vries equation arises to describe evolution of plasma waves or the propagation of transverse. In this paper, we give a classification of group invariant solutions for the CMKdV equation by using classic ..."
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The complex modified Kortewegde Vries (CMKdV) equation which can reduce to modified Kortewegde Vries equation arises to describe evolution of plasma waves or the propagation of transverse. In this paper, we give a classification of group invariant solutions for the CMKdV equation by using
Supersymmetric Modified Kortewegde Vries Equation: Bilinear Approach
, 2004
"... A proper bilinear form is proposed for the N = 1 supersymmetric modified Kortewegde Vries equation. The bilinear Bäcklund transformation for this system is constructed. As applications, some solutions are presented for it. 1 ..."
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Cited by 1 (0 self)
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A proper bilinear form is proposed for the N = 1 supersymmetric modified Kortewegde Vries equation. The bilinear Bäcklund transformation for this system is constructed. As applications, some solutions are presented for it. 1
Selfsimilar planar curves related to modified Kortewegde Vries equation
 J. Differential Equations
"... Abstract We exhibit a time reversible geometric flow of planar curves which can develop singularities in finite time within the uniform topology. The example is based on the construction of selfsimilar solutions of modified Kortewegde Vries equation of a given (small) mean. ..."
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Cited by 5 (0 self)
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Abstract We exhibit a time reversible geometric flow of planar curves which can develop singularities in finite time within the uniform topology. The example is based on the construction of selfsimilar solutions of modified Kortewegde Vries equation of a given (small) mean.
∂x = 0. Modified Korteweg–de Vries equation.
"... 1◦. Onesoliton solution for σ = 1: w(x, t) = a + k 2 4a2 + k2 cosh z + 2a, z = kx − (6a2k + k3)t + b, where a, b, and k are arbitrary constants. 2◦. Twosoliton solution for σ = 1: w(x, t) = 2 a1e θ1 + a2eθ2 + Aa2e2θ1+θ2 + Aa1eθ1+2θ2 1 + e2θ1 + e2θ2 + 2(1 − A)eθ1+θ2 + Ae2(θ1+θ2), θ1 = a1x − a 3 1 ..."
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1◦. Onesoliton solution for σ = 1: w(x, t) = a + k 2 4a2 + k2 cosh z + 2a, z = kx − (6a2k + k3)t + b, where a, b, and k are arbitrary constants. 2◦. Twosoliton solution for σ = 1: w(x, t) = 2 a1e θ1 + a2eθ2 + Aa2e2θ1+θ2 + Aa1eθ1+2θ2 1 + e2θ1 + e2θ2 + 2(1 − A)eθ1+θ2 + Ae2(θ1+θ2), θ1 = a1x − a 3 1t + b1, θ2 = a2x − a
The wellposedness of Cauchy problem for dissipative modified Korteweg de
, 2007
"... Abstract. In this paper we consider some dissipative versions of the modified Korteweg de Vries equation ut +uxxx +Dx  α u+u 2 ux = 0 with 0 < α ≤ 3. We prove some wellposedness results on the associated Cauchy problem in the Sobolev spaces H s (R) for s> 1/4 − α/4 on the basis of the [k; Z ..."
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Cited by 2 (1 self)
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Abstract. In this paper we consider some dissipative versions of the modified Korteweg de Vries equation ut +uxxx +Dx  α u+u 2 ux = 0 with 0 < α ≤ 3. We prove some wellposedness results on the associated Cauchy problem in the Sobolev spaces H s (R) for s> 1/4 − α/4 on the basis of the [k
Numerical Simulations of the Complex Modified Kortewegde Vries Equation
"... In this paper implementations of three numerical schemes for the numerical simulation of the complex modified Kortewegde Vries (CMKdV) equation are reported. The first is an integrable scheme derived by methods related to the Inverse Scattering Transform (IST). The second is derived from the first ..."
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Cited by 2 (1 self)
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In this paper implementations of three numerical schemes for the numerical simulation of the complex modified Kortewegde Vries (CMKdV) equation are reported. The first is an integrable scheme derived by methods related to the Inverse Scattering Transform (IST). The second is derived from the first
ON THE CAUCHY PROBLEM FOR THE MODIFIED KORTEWEG–DE VRIES EQUATION WITH STEPLIKE FINITEGAP INITIAL DATA
"... Abstract. We solve the Cauchy problem for the modified Korteweg–de Vries equation with steplike quasiperiodic, finitegap initial conditions under the assumption that the perturbations have a given number of derivatives and moments finite. 1. ..."
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Cited by 6 (3 self)
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Abstract. We solve the Cauchy problem for the modified Korteweg–de Vries equation with steplike quasiperiodic, finitegap initial conditions under the assumption that the perturbations have a given number of derivatives and moments finite. 1.
Results 1  10
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159