Under the assumption that u ' is a function form of e inu , this paper presents a new set of traveling-wave solutions with JacobiAmplitude function for the generalized form of the double Sine-Gordon equation u tt = ku xx + 2 α sin ( nu ) + β sin ( 2 nu ) .

ResearchArticle New Travelling Wave Solutions for Sine-Gordon Equation YunchuanSun BusinessSchool,BeijingNormalUniversity,Beijing100875,China

Finding solutions to Equation 2.6 may be easy or difficult depending on the polarization term. O. E. Martinez, J. P. Gordon and R. L. Fork. Negative (3.3 fs) cosine and sine pulses are plotted and compared to two-colour derivation of the model equations occurs, followed by a numerical solution. because an analytic dots standing for d2 =dt2 , and so on. Superscripted Explore how the sine{Gordon solitary waves vary in shape as the velocity c is. altered.

Some New Exact Traveling Wave Solutions of Double-sine-Gordon Equation. February 2008; Communications in Theoretical Physics 49(2):303 New Travelling Wave Solutions for Time-Space Fractional Liouville and Sine-Gordon Equations 3 1 Definition 2. Let a 0 , ta , (,]g be a function defined on at and . Then, 2 the th order fractional integral of function g is defined as (Khalil et al., 2014), 1 () . t ta a gx Igt dx x 3 2006-07-01 · Li and Chen studied bifurcations of travelling wave solutions of the following double Sine–Gordon equation (1.5) u xt = sin (u) + sin (2 u). In this paper, we consider the following general Sine–Gordon equation (1.6) u tt - u xx + α sin ( u ) + β sin ( 2 u ) = 0 , where α , β are constants and ( α , β ) ≠ (0, 0). equations (Tang, 2010), the solutions of the combined sine-cosine-Gordon equation were studied by the variable separated ODE method (Kuo, 2009).

travelling wave solutions for a more general sine-Gordon equation: = + sin ( ). ( ) In this paper, a method will be employed to derive a set of exact travelling wave solutions with a JacobiAmplitude function form which has been employed to the Dodd-Bullough equation and some new travelling wave solutions have been derived [ ].

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Sine gordon equation travelling wave solution

(~ sine-Gordon ~> equation [2] (SGE) rather than the (~ nonlinear Klein-Gordon , > equation SGE are the travelling waves or (~ waves of permanent profile ~) of the form. (2.4) Thus any solution of (1.1) for which the independ

We have the following theorem: Theorem 1. Kink wave solutions to equation (1) utt = uxx + … Request PDF | On Jul 3, 2020, S. P. Joseph published TRAVELING WAVE EXACT SOLUTIONS FOR GENERAL SINE-GORDON EQUATION | Find, read and cite all the research you need on ResearchGate in the form of traveling wave φ(x,t)=U(θ), θ=x−c0t. Then the sine-Gordon equation will take the form (c02−1)Uθθ+sin⁡U=0. In this chapter, a series of mathematical transformations is applied to the sine-Gordon equation in order to convert it to a form that can be solved. The new form appears to be considerably more complicated than the original; however, it readily yields a traveling wave solution by application of the tanh method. For example, the travelling wave solutions of the (1+2)-dimensional Kadomtsev-Petviashvili II equation (KP II) are solitons, and those of the higher-dimensional Sine-Gordon equation are fronts.

Key words: discrete sine-Gordon equation, exact travelling wave solution, extended tanh-function approach. Feb 11, 2020 traveling wave solutions of the (2+1)-dimensional sinh-Gordon equation can also be provided in a Leibbrandt [12] studied solutions of the sine-Gordon equation in which gives us the following single kink wave solut derivative term in the sine- Gordon equation allows one to generate the same Gordon equation does not possess exact bell-shaped traveling wave solution [1, Sine-Gordon equations by using a reliable analytical method called New Travelling Wave Solutions for Time-Space Fractional the following solution sets .
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Knowing ω we can calculate the May 23, 2020 (d) waht is the maximum transverse speed of an element of the string? check- circle. Text Solution.
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Sine-Gordon equations by using a reliable analytical method called New Travelling Wave Solutions for Time-Space Fractional the following solution sets . 26.

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Gorbachev Gordan/M Gorden/M Gordian/M Gordie/M Gordimer/M Gordon/M Wauwatosa/M Wave/S Waveland/M Waverley/M Waverly/M Way/M Waylan/M anorexia/MS anorexic/S another/M ans/M answer/ZUDGRMSB answerer/M equalize/DRSUZGJ equalizer/M equanimity/MS equate/SDNGXB equation/M

In this research, the Homotopy-Perturbation Method (HPM) has been used for solving sine-Gordon and coupled sine-Gordon equations, which have a wide range of applications in We use the tanh method and a variable separated ODE method for solving the double sine-Gordon equation and a generalized form of this equation. Several exact travelling wave solutions are formally For example, the travelling wave solutions of the (1+2)-dimensional Kadomtsev-Petviashvili II equation (KP II) are solitons, and those of the higher-dimensional Sine-Gordon equation are fronts.

2010-10-13 · Abstract: We give a geometric proof of spectral stability of travelling kink wave solutions to the sine-Gordon equation. For a travelling kink wave solution of speed $c eq \pm 1$, the wave is spectrally stable. The proof uses the Maslov index as a means for determining the lack of real eigenvalues. Ricatti equations and further geometric considerations are also used in establishing stability.

ere nedenfor, nemlig hans hjelpsom het overfor sine tilhengere (sine venner). N either Hellberg nor H ødnebø has presented a convincing solution of this problem. Yet this m etaphor (and the equation of a ship w ith a bear m ust be either a m eta word and a sea or a wave word m ust all be treated as approxim ately Hence we can replace z by z +z0, where z0 is any constant, in the above solutions of equation (1.4).

Title Authors Introduction sine-Gordon Lax system Numerical Sine-Gordon Equation The sine-Gordon equation is a nonlinear hyperbolic partialdifferential equation in-volving the d’Alembert operator and the sine of the unknown function. Let us look for travelling wave solutions of the sine-Gordonequation (5.1) of the form u(ξ):=u(x−ct), 45.