In this work, we will concentrate on constructing novel forms of soliton solution for the Lonngren Wave Equation. The Lonngren Wave Equation is important in areas where understanding wave phenomena is critical, including engineering, physics, and applied mathematics. It allows for analysis and prediction of wave behaviour under various physical conditions. These forms of soliton solution will be obtained using two of the recent efficient analytic techniques, one of them is the Riccati-Bernoulli Sub-OD Equation method, which is not obeys to the principle of homogenous balance. The other analytic method which obeys the homogenous balance principle is the extended simple equation method. Besides the two analytic methods, we introduce the approximate solutions corresponding to the soliton solutions obtained before by the mentioned analytic methods using the numerical technique called the Haar Wavelet Method. With the help of Mathematica program, the 2D and 3D graphs are considered to explain the physical and geometric interpretations of the obtained results. The obtained solitons are of the kind periodic parabolic soliton solution, bright soliton solution, dark soliton solution, kink soliton solution. Our results are obtained for the first time, and they are important and effective compared to the results obtained by other authors for the same problem. |
