| [1] Christov C I, Marinov T T, Marinova R S. Identification of solitary-wave solutions as an inverse problem: Application to shapes with oscillatory tails. Math Comp Simulation, 2009, 80: 56-65
[2] Mishkis A D, Belotserkovskiy P M. On resonance of an infinite beam on uniform elastic foundation. ZAMM-Z Angew Math Mech, 1999, 79: 645-647
[3] Porubov A. Amplification of Nonlinear Strain Waves in Solids. World Scientific, 2003
[4] Samsonov A M. Strain Solitons in Solids and How to Construct Them. Chapman and Hall/CRC, 2001
[5] Maugin G A. Nonlinear Waves in Elastic Crystals. Oxford University Press, 1999
[6] Falk F, Laedke E W, Spatschek K H. Stability of solitary-wave pulses in shape-memory alloys. Phys Rev B, 1987, 36(6): 3031-3041
[7] Tao T, Visan M, Zhang X. The nonlinear Schrödinger equation with combined power-type nonlinearities. Comm Partial Differential Equations, 2007, 32: 1281-1343
[8] Payne L E, Sattinger D H. Saddle points and instability of nonlinear hyperbolic equations. Israel J Math, 1975, 22(3/4): 273-303
[9] Kutev N, Kolkovska N, Dimova M. Global behavior of the solutions to Boussinesq type equation with linear restoring force. AIP CP, 2014, 1629: 172-185
[10] Xu R. Cauchy problem of generalized Boussinesq equation with combined power-type nonlinearities. Math Meth Appl Sci, 2011, 34: 2318-2328
[11] Liu Y, Xu R. Potential well method for Cauchy problem of generalized double dispersion equations. J Math Anal Appl, 2008, 338: 1169-1187
[12] Polat N, Ertas A. Existence and blow up of solution of Cauchy problem for the generalized damped multidimensional Boussinesq equation. Math Anal Appl, 2009, 349: 10-20
[13] Wang S, Chen G. Cauchy problem of the generalized double dispersion equation. Nonlinear Anal, 2006, 64: 159-173
[14] Yang Zhijian, Guo Boling. Cauchy problem for the multi-dimensional Boussinesq type equation. J Math Anal Appl, 2008, 340: 64-80
[15] Straughan B. Further global nonexistence theorems for abstract nonlinear wave equations. Proc Amer Math Soc, 1975, 48: 381-390
[16] Liu Y. Instability and blow up of solutions to a generalized Boussinesq equation. SIAM J Math Anal, 1995, 26: 1527-1546
[17] Levine H A. Instability and nonexistence of global solutions to nonlinear wave equations of the form Putt=Au+F(u). Trans Amer Math Soc, 1974, 192: 1-21
[18] Kalantarov V K, Ladyzhenskaya O A. The occurrence of collapse for quasilinear equations of parabolic and hyperbolic types. J Soviet Math, 1978, 10(1): 53-70 |