Herbart's fourth and gravest complaint is that the theory of faculties ignores the particular, and neglects exact description, the sine qua non of empirical science (PsW: 27).
In Section 3, the method is employed for obtaining the exact solutions of double sine-Gordon (SG) and Burgers equations, and finally conclusions are presented in Section 4.
Solutions for various whirling-type motions are found, including precessing elliptical whirling of an approximate sine arc and exact solutions for circular whirling involving elliptic integrals and embracing high modes.
Therefore, the exact solutions to the double sine-Gordon (SG) equation can be written as (25).
On the other hand, of the 684 repeat arrays in non-masked clones, 181 were imperfect and this number was not significantly different from the number calculated for tRNA SINEs (156 imperfects, Fisher's exact test, P =.2928) and for other repeats (115 imperfects, Fisher's exact test, P =.3613).
A specific SINE insertion site is delimited by the exact sequence of the 6 20 base pair target site duplication (TSD).
aFisher's exact test for comparisons between specific motifs in tRNA SINE and the combined values of the other two databases.
The number of compounds was not significantly different from that calculated from the tRNA SINE (46 compounds in 330 clones, Fisher's exact test, P =.263) and other repeats (50 compounds in 357 clones, Fisher's exact test, P =.249) databases.
In this paper, we utilize this method and obtain exact solutions of two nonlinear partial differential equations, namely double sine-Gordon and Burgers equations.
Yan and Zhang [28] obtained new explicit and exact traveling wave solutions for Eq. (1) by an improved sine-cosine method and the Wu elimination method.
The exact phase distributions can be easily calculated by digitally fitting the background fringes to sine waves, and the temporal phase-shift errors can be avoided.
