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Content
Volume 31 (2024)
Volume 31, Issue 2 (In progress)
Pg 63 - 92 (December 2024)
Volume 31, Issue 1
Pg 1 - 61 (June 2024)
Volume 30 (2023)
Volume 30, Issue 2
Pg 107 - 185 (December 2023)
Volume 30, Issue 1
Pg 1 - 105 (June 2023)
Volume 29 (2022)
Volume 29,
Pg 1 - 58 (December 2022)
Volume 28 (2022)
Volume 28,
Pg 1 - 58 (June 2022)
Volume 27 (2021)
Volume 27, Issue 2
Pg 67 - 90 (December 2021)
Volume 27, Issue 1
Pg 1 - 65 (September 2021)
Volume 26 (2021)
Volume 26, Issue 2
Pg 85 - 140 (June 2021)
Volume 26, Issue 1
Pg 1 - 84 (March 2021)
Volume 25 (2020)
Volume 25, Issue 2
Pg 67 - 140 (October 2020)
Volume 25, Issue 1
Pg 1 - 66 (July 2020)
Volume 24 (2020)
Volume 24, Issue 1-2
Pg 1 - 55 (April 2020)
Volume 23 (2019)
Volume 23, Issue 2
Pg 119 - 214 (October 2019)
Volume 23, Issue 1
Pg 1 - 118 (July 2019)
Volume 22 (2019)
Volume 22, Issue 2
Pg 101 - 204 (April 2019)
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Pg 1 - 100 (January 2019)
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Volume 21, Issue 4
Pg 389 - 587 (October 2018)
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Pg 279 - 388 (July 2018)
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Pg 127 - 278 (April 2018)
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Pg 1 - 125 (January 2018)
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Volume 20, Issue 4
Pg 457 - 625 (October 2017)
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Pg 335 - 456 (July 2017)
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Pg 211 - 334 (April 2017)
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Volume 19, Issue 4
Pg 725 - 937 (October 2016)
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Pg 489 - 723 (July 2016)
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Pg 203 - 488 (April 2016)
Volume 19, Issue 1
Pg 1 - 201 (January 2016)
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Pg 163 - 343 (October 2015)
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Pg 1 - 162 (July 2015)
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Volume 17, Issue 2
Pg 135 - 283 (April 2015)
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Pg 1 - 134 (January 2015)
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Volume 16, Issue 2
Pg 163 - 251 (October 2014)
Volume 16, Issue 1
Pg 1 - 98 (July 2014)
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Volume 15, Issue 2
Pg 101 - 208 (April 2014)
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Pg 1 - 100 (January 2014)
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Pg 147 - 283 (October 2013)
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Pg 1 - 145 (July 2013)
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Volume 13, Issue 2
Pg 75 - 156 (April 2013)
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Pg 1 - 74 (January 2013)
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Pg 81 - 147 (October 2012)
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Pg 1 - 80 (July 2012)
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Pg 73 - 161 (April 2012)
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Pg 1 - 72 (January 2012)
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Pg 79 - 169 (October 2011)
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Pg 1 - 77 (July 2011)
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Pg 77 - 149 (April 2011)
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Pg 1 - 76 (January 2011)
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Pg 99 - 211 (October 2010)
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Pg 1 - 97 (July 2010)
Volume 7 (2010)
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Pg 81 - 188 (April 2010)
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Pg 1 - 80 (January 2010)
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Pg 103 - 195 (October 2009)
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Pg 1 - 101 (July 2009)
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Volume 5, Issue 2
Pg 107 - 218 (April 2009)
Volume 5, Issue 1
Pg 1 - 106 (January 2009)
Volume 4 (2008)
Volume 4, Issue 2
Pg 117 - 228 (October 2008)
Volume 4, Issue 1
Pg 1 - 115 (July 2008)
Volume 3 (2008)
Volume 3, Issue 2
Pg 105 - 237 (April 2008)
Volume 3, Issue 1
Pg 1 - 103 (January 2008)
Volume 2 (2007)
Volume 2, Issue 2
Pg 117 - 238 (October 2007)
Volume 2, Issue 1
Pg 1 - 115 (July 2007)
Volume 1 (2007)
Volume 1, Issue 2
Pg 101 - 205 (April 2007)
Volume 1, Issue 1
Pg 1 - 100 (January 2007)
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Advances and Applications in Fluid Mechanics
Advances and Applications in Fluid Mechanics
Volume 9, Issue 1, Pages 1 - 16 (January 2011)
SOLITARY WAVES, PERIODIC AND ELLIPTIC SOLUTIONS TO THE BENJAMIN, BONA AND MAHONY EQUATION MODIFIED BY VISCOSITY
Stefan C. Mancas, Harihar Khanal and Shahrdad G. Sajjadi
Abstract:
In this paper, we use a traveling wave reduction or a so-called spatial approximation to comprehensively investigate periodic and solitary wave solutions of the modified Benjamin. Bona and Mahony equation (BBM) to include both dissipative and dispersive effects of viscous boundary layers. Under certain circumstances that depend on the traveling wave velocity, classes of periodic and solitary wave like solutions are obtained in terms of Jacobi elliptic functions. An ad-hoc theory based on the dissipative term is presented, in which we have found a set of solutions in terms of an implicit function. Using dynamical systems theory we prove that the solutions of (1.6) experience a transcritical bifurcation for a certain velocity of the traveling wave. Finally, we present qualitative numerical results.
Keywords and phrases:
viscous water waves, solitary waves, solitons, Hamiltonian.
Communicated by K. K. Azad
Number of Downloads:
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P-ISSN: 0973-4686
Journal Stats
Publication count:
368
Citation count (Google Scholar):
1124
h10-index (Google Scholar):
24
h-index (Google Scholar):
16
Downloads :
110409
Views:
393777
Downloads/publish articles:
300.02
Citations (Google Scholar)/publish articles:
3.05
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