%0 Journal Article %1 Lonngren1975538 %A Lonngren, K. E. %A Hsuan, H. C. S. %A Ames, W. F. %D 1975 %J Journal of Mathematical Analysis and Applications %K Soliton %N 3 %P 538 - 545 %R 10.1016/0022-247X(75)90078-5 %T On the soliton, invariant, and shock solutions of a fourth-order nonlinear equation %U http://www.sciencedirect.com/science/article/B6WK2-4CRJ2XH-1DX/2/2c75e0c089d6a40815d4caa7250e0af3 %V 52 %X A particular transmission line containing a nonlinear capacitance is shown to satisfy the equation Vxxtt + omega02Vxx - Cs-1VCn(V)tt = 0, omega02 = (LCS)-1. This equation is shown to permit the propagation of solitary waves (solitons). In addition, it admits an invariant (similar) solution under the spiral group. Lastly, we demonstrate two implicit traveling wave solutions that permit the evolution of a discontinuity in the first derivatives (shocks).

@article{Lonngren1975538, abstract = {A particular transmission line containing a nonlinear capacitance is shown to satisfy the equation Vxxtt + [omega]02Vxx - Cs-1[VCn(V)]tt = 0, [omega]02 = (LCS)-1. This equation is shown to permit the propagation of solitary waves (solitons). In addition, it admits an invariant (similar) solution under the spiral group. Lastly, we demonstrate two implicit traveling wave solutions that permit the evolution of a discontinuity in the first derivatives (shocks).}, added-at = {2011-02-13T23:40:34.000+0100}, author = {Lonngren, K. E. and Hsuan, H. C. S. and Ames, W. F.}, biburl = {https://www.bibsonomy.org/bibtex/2a529712376fa88137152036a7e79ea7d/casvada}, description = {ScienceDirect - Journal of Mathematical Analysis and Applications : On the soliton, invariant, and shock solutions of a fourth-order nonlinear equation*1}, doi = {10.1016/0022-247X(75)90078-5}, interhash = {8f46160eb8329ebf46fb4d82c4731405}, intrahash = {a529712376fa88137152036a7e79ea7d}, issn = {0022-247X}, journal = {Journal of Mathematical Analysis and Applications}, keywords = {Soliton}, number = 3, pages = {538 - 545}, timestamp = {2011-02-13T23:40:34.000+0100}, title = {On the soliton, invariant, and shock solutions of a fourth-order nonlinear equation}, url = {http://www.sciencedirect.com/science/article/B6WK2-4CRJ2XH-1DX/2/2c75e0c089d6a40815d4caa7250e0af3}, volume = 52, year = 1975 }