Sentence examples for traveling solution from inspiring English sources

From the results in Theorem 4.3, we know that the wave speed is unique, and thus, the unique traveling solution to equation (1.1) exists when θ ∈ ( φ ( c ), α 2 + φ ( c ) ].

Substituting the values of (R1, Q1, P1) and the corresponding Jacobi F chosen from "Appendix 1" into the general form of the traveling solution Eq. (64), we can simultaneously obtain different periodic wave solutions to the elliptic-like Eq. (1).

end{aligned} It is obvious that F is well defined and a fixed point of F is a solution of (3.1), which is a traveling solution of (2.1) connecting ((0,0)) and ((k_{1},k_{2})) if it satisfies (3.3).

Furthermore, we obtained a very general class of exact solutions of the KdV-Sawada-Kotera-Ramani equation (1.1), which included the solitary wave solutions, periodic and quasi-periodic traveling wave solutions and some unbounded traveling solutions as well.

We consider both the steady state and the two-periodical traveling solutions of the counter-current gas/liquid flow between the corrugated plates.

Bilinear equation, N-soliton solutions, traveling wave solutions and multi-symplectic structure are obtained by applying the proposed method to the KdV equation.

Bilinear equation or homogeneous equation, N-soliton solutions, traveling wave solutions and multi-symplectic structure are obtained respectively by applying the proposed method to the KdV equation.

If no traveling wave solution exists, every positive solution of (1) converges to zero for t → ∞, uniformly in x.

In [30, 32], the authors have given the traveling waves solution, peaked solitary wave solutions for (1.3).

The exact solutions obtained were traveling wave solutions, cnoidal and snoidal wave solutions.

The efficiency of this method for finding exact solutions and traveling wave solutions has been demonstrated.